1
MODULE-4
ULTRASONICS
Introduction
Sounds waves are mechanical vibrations of smaller amplitude. Based on their
frequencies sound waves are classified into three categories.

Sounds waves of frequencies between 20Hz and 20,000Hz.These sounds
are audible.

Sounds waves of frequencies below 20Hz. These are inaudible and called
as infrasonics.

Sound waves of frequencies above 20,000Hz.These are also inaudible
and called as ultrasonics.
So,Ultrasonics are the sound waves having frequencies greater than
20,000Hz.As human ear is sensitive only for the sound waves of frequencies
ranging from 20 Hz to 20,000Hzit cannot sense ultrasonic sounds but dogs
and other animals can hear the high frequency sounds. Bats and dolphins are
known to generate ultrasonic waves and use reflections of the waves to find
their way.
Due to small wavelength, noiseless performance and directional property,
these waves are preferred over audible sound. Ultrasonic waves are widely
used in medical diagnostics, marine applications, nondestructive testing and
other engineering applications.
The ultrasonic waves are produced by the following methods,
namely
(1)mechanical generator Or Galton’s whistle
(2) Electrical Generators
a) magnetostriction method
b) piezoelectric method.
The magnetostriction method is based on the principle of magnetostriction
effect. The piezoelectric method is based on the principle of piezoelectric effect.
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TYPES OF ULTRASONIC WAVES
Ultrasonic waves are classified into four types based on their propagation
through the medium.

Transverse ultrasonic waves Or Shear waves

Longitudinal Or compressional ultrasonic waves

Surface Or Reyleigh waves

Lamb waves Or plate waves
1)
Transverse ultrasonic Waves
In the transverse ultrasonic waves , the particle of the medium vibrates
perpendicular to the direction of the propagation of the wave.
The transverse wave is also called shear wave.The velocity of transverse
ultrasonic wave is nearly 50% of the velocity of the longitudinal ultrasonic wave
in the medium. The velocity of the shear wave is given by
vT 


3
where‘ ’ is the rigidity modulus of the medium and  is the density of the
medium. The transverse wave can propagate only in solids, because in liquids
and gases, this type of wave is greatly attenuated.
2)
Longitudinal Ultrasonic Waves
In this waves the particle of the medium vibrates parallel to the direction of
the propagation of the wave.
The velocity of longitudinal wave propagating through a solid material is given
by
VL 
Y

Where Y is the Young’s modulus and  is the density of the solid.
The Ultrasonic wave produces alternate compression and rarefraction while
passing through the liquid Or gaseous medium. Longitudinal motion is most
common form of sound transmission. The longitudinal wave can propagate in
solids, liquids and gases.
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3)
Surface Or Rayleigh Waves
In certain elastic medium, the ultrasonic wave passes only along the surface of
the medium and hence they are called surface wave Or Rayleigh wave.The
surface wave were first discovered by Rayleigh hence they are also known as
Rayleigh waves.The surface wave doesnot propagate through the entire
thickness of the material. The surface waves are used to study about the
surface defects in the materials.The surface waves are analogous to water
waves created on the surface of the water. The particle in the water wave
vibrate both in the longitudinal and transverse waves whereas in Rayleigh
waves the particles are having elliptical vibration.The velocity of the surface
wave is,
V=0.9VT, where VT is the velocity of the transverse wave.
4)
Plate Or Lamb Waves
When the thickness of the medium is equal to one wavelength, the surface
wave does not exist and the medium vibrates whenever the ultrasonic waves
passed through it.This type of wave is said to be plate wave Or Lamb wave.
The Lamb wave occurs in two different modes, namely(1)Symmetrical mode
and (2) Asymmetrical mode
If the displacement of the particles is elliptical on the surface and longitudinal
in nature, then it is said to be symmetrical Lamb wave. If the displacement is
elliptical on the surface and transverse in nature then it is said to be
asymmetrical lamb wave. The velocity of the Lamb wave depends on the
frequency , incident angle, thickness and the material property, whereas the
velocity of the longitudinal,transverse and surface waves depends on the
material property alone.
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GENERATION Or PRODUCTION OF ULTRASONICS
In general ultrasonic waves are generated by the following three method.



Mechanical Generator Method
Magnetostriction Method
Piezoelectric effect Method
Mechanical Generators
Mechanical generators may be further subdivided into two groups.

Gas driven: The are simple divices to produce ultrasonics of frequencies
up two 30kHz, such as Galton’s whistle and siren etc.

Liquid driven: These are transducer type devices which convert energy
from one form to another, such as vibrating blade transducer and
hydrodynamic oscillator. A carbon microphone is also an example of
transducer in audible range.
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Electrical Generators
They are widely used nowadays for producing Ultrasonics and are subdivided
into two categories.
1) Piezoelectric Generators Or Piezoelectric Transducer
Or
Pressure Electricity Effect
Langevin in 1917 devised a method for producing Ultrasonics by the use of
piezoelectric effect. He used an electric oscillatory circuit to provide e.m.f and
the tuning is achieved by a variable condenser.
When certain crystal(such as quartz, tourmaline and rochellesalt) are
subjected to pressure (either compression Or expansion) they exhibit opposite
electrical charges on their opposite faces resulting in a potential difference.
This phenomenon is known as Piezoelectric effect. Conversely, if the opposite
sides of these crystals are maintained at different electrical potentials by
applying a voltage, then the crystals slice expands Or contracts.Then
phenomenon known as converse Piezoelectric effect Or Inverse piezoelectric
effect is utilized in the production of ultrasonic waves of high frequency.
Piezo electric effectInverse Piezoelectric effect
1)
Magnetostriction Oscillator
Magnetostriction is the property by which a ferromagnetic material (like nickel,
cobalt, iron) in the form of a rod changes in length when placed in a magnetic
field parallel to its length. This phenomenon can be used to produce
Ultrasonics.
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Piezoelectric Effect
Piezoelectricity derives its name from the Greek word ‘Piezo’ which means
pressure and hence a literal translation would be pressure electricity.
Whenever a Piezoelectric crystal is subjected to pressure Or squeezing Or
twisting , the electric charges are developed Or p.d is developed in the other
two faces of the crystals. The magnitude of p.d developed across the crystal is
proportional to the extent of deformation produced. This effect Or
phenomenon is known as Piezoelectric effect Or direct ‘ Piezoelectric effect ‘.
The converse of this effect is also found to be true. Instead of applying
pressure, if a Piezoelectric crystal is subjected to a dc electric field, the
dimension of the crystal changes. i.e , the dimension either increases Or
decreases. If the polarity of electric field is reversed, the changes in dimension
also reversed. Instead of applying a d.c electric field, if an a.c field is applied ,
the dimensions changes continuously. During one half cycle of the electric
field, the dimension of the crystal increases and the other half cycle of the
electricfield, the dimension of the crystal decreases. Therefore, whenever an
alternating electric field is applied to a Piezoelectric crystal, the dimension of
the crystal changes continuously and hence the crystal is set into vibration.
This phenomenon is known as Inverse Piezoelectric Effect.
Piezo electric effectInverse Piezoelectric effect
The above two effects are the basis of Piezoelectricity. This history of
Piezoelectricity dates back to 1880 when Pierre Curie and Jacques Curie first
discovered the Piezoelectric effect in substance like the naturally occurring
quartz, tourmaline and Rochelle salt crystals. Quartz is found to occur as
colourless Silicon dioxide(SiO2) while tourmaline is a red , pink, green, blue,
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yellow ,brown, black Or colourless Silicate. Rochelle salt can be crystallized
from a solution of Potassium Sodium Titrate.
In 1940, the first synthetic piezoelectric substance, barium titanate made its
appearance. It has Piezoelectric activity nearly comparable to Rochelle salt, i.e,
the voltage developed under pressure is of approximately the same magnitude
and the change in the size of the crystal when a voltage is applied are also
similar. Further, barium titanate offers some additional advantages in that it
is not water soluble and can withstand higher operating temperatures. Also it
can be fabricated to any Physical shape. Since then, lithium Sulphate, Lead
Zircontetitanate and leadmeta-niobate have also been used as Piezoelectric
materials.
It would now be obvious that if an alternating voltage is applied across a slice
of quartz crystal, it would begin to alternately contract and expand and hence
start vibrating. If the frequency of the applied alternating voltage happens to
be equal to that of the natural frequency of the quartz crystal, the later will
thrown into resonant vibration and hence produce ultrasonics.
Quartz Crystal
The production of ultrasonic waves by Piezoelectric generators depends upon
the Piezoelectric effect. Consider a common form of Silica and is found in the
form of a hexagonal prism with hexagonal pyramids at both the ends.
The axis joining two crowns Or pointed ends of the crystal is known as the
optical Or Z-axis. The three axes XX,X1X1,X11 X11 passing through the
corner of the hexagon are known as the X-axes Or electrical axes. The
three axes YY, YY, YY which are perpendicular to the face of the crystal
and are at right angles to the respective electrical axes are known as Yaxes Or mechanical axes Or The line joining the midpoint of the opposite
faces of the crystal is known as Y-axis.
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When the quartz is subjected to mechanical stress along the Y-axis electrical
charges appear on the faces of the crystal perpendicular to the axis i.e, along
X-axis.
Conversely, if electrical charges are placed along the faces perpendicular to Xaxis a mechanical strain and change in dimensions, i.e expansion Or
contraction is produced along X-axis.
This plates of Quartz crystal cut perpendicular to an X-axis are known as Xcut crystal plates. Similarly, thin quartz plates cut perpendicular to a Y-axis
are known as Y-cut crystal plates. An X-cut crystal has a negative temperature
coefficient, ie, an increase in temp. causes the resonant frequency to decrease.
The Y-cut crystal on the other hand has a positive temperature coefficient. It is
then possible to obtain crystal pieces having zero tem. Coefficient by cutting
the crystal at an angle intermediate b/w X and Y cut. There are three types of
such crystals having zero tem. Coefficient. These are AT cut, CT cut and GT
cut.
An AT-cut crystal is cut from a plane which is rotated about an X-axis such
that an angle   35.5 0 is made with Z- axis. It is widely used for the generation
of voltages having frequencies ranging from 500 kHz to 10MHz. A CT-cut
crystal is suitable for generation of voltages having frequencies in the range of
50–200 kHz. It is a square in shape and is cut from a plane. So that the angle
 made with the Z-axis is approximately 37.50. But these crystals have zero
temp. coefficientonlt for small operating ranges. Hence, GT cut crystal is
widely used which is essentially constant in frequency over the range of 00C –
1000C. It is regular in shape with width equal to 0.855 times of its length and
is cut from a plane making an angle  of 51.5 0 with Z- axis. The resonant
frequency of a crystal depends mainly upon its thickness and cut. For X- cut
and AT cut crystals, the length and breadth are of relatively minor importance
and the frequency is given by
K
f  kHz
t
Where ‘t’ is the thickness of the crystal plate in mm and K is a constant the
value of which is 2730 for X-cut 1960 for Y-cut and 1650 for AT cut crystal.
The frequency of resonance of a CT- cut crystal is
3100
f 
kHz
x
Where ‘x’ is the length of each side of square crystal in mm.
The frequency of resonance of GT- cut crystal is given by
3292
f 
kHz
w
Where ‘w’ is the width of GT-plate in mm.
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Piezoelectric Oscillator
a)
Principle
The Piezoelectric Oscillator is based on the principle of Piezoelectriceffect.i.e,
inverse piezo electric effect. When an alternating electric field(alternating
voltage) of definite frequency is applied to a crystal along certain axis , the
crystalexpands and contracts. It is set into mechanical vibration of the tank
circuit and hence it produces Ultrasonic waves.
b)
Construction
The coil L1, L2 and L3 arecoupled together by means of transformer action. A
variable capacitorC1 , is connected parallel to the coil L1. One end of the
variable capacitor is connected to the collector of the NPN transistor and the
other end is connected to a battery through milliammeter and a key K. One
end of the coil L2 is connected to a battery through a milliammeter and a key
K. One end of the coil L2 is connected to the base of the NPN transistor,
whereas the other end is connected to the emitter and the negativeterminal of
the battery.
The Piezoelectric Oscillator is shown in fig.
c)
Working
1.
The key K is closed and hence the tank circuit is set into vibration. The
frequency of vibration of tank circuit is given by
11
f 
1
2 L1C1
Where L1 and C1 are the inductance of the coil and capacitance of the
capacitor respectively.
2.
The oscillation of the tank circuit produces an alternating e.m.f in the
tank circuit.
3.
An e.m.f is induced by mutual induction in the coil L2. This e.m.f is fed
into transistor as an input into the base-emitter terminal. The transistor is
used to ensure the correct phase of the feed back.
4.
The input is amplified and fed into the collector circuit.
5.
Due to transformer action an emf is induced in the coil L3.
6.
The induced emf is applied to the piezoelectric crystal. Due to this
alternating emf, the piezoelectric crystal is set into continuous vibration.
7.
When the frequency of the oscillation i.e the frequency of the tank
circuit coincides with the frequency of the piezoelectric crystal,the resonance
vibration takes place.
8.
During the resonant
vibration,
the
piezoelectric
crystal
producesUltrasonic Waves.
The condition for resonance is,
Frequency of the oscillator circuit= Frequency of the Crystal.
1
1 Y

2 L1C1 2l 
The frequency of the ultrasonic waves produced when the crystal is placed
along its thickness b/w the plates A & B is given by
1 Y
f 
2t 
The frequency of the ultrasonic waves produced when the crystal is placed
along its length b/w the plate A and B is given by
1 Y
n Y
f 
f 
2l 
2l  i.e ,
n=1,2,3 etc. for fundamental mode , first overtone,
second overtone etc.
Where ‘t’ is the thickness of the crystal ‘l’ is the length of the crystal, Y is the
Young’s modulus of the piezoelectric crystal and ‘  ’ is the density of the
Piezoelectric crystal.
V Y

Where ‘Y’ is the Young’s modulus of the piezoelectric crystal and ‘  ’ is the
density of the Piezoelectric crystal.
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d)
Advantages
1.
The maximum frequency of the ultrasonic wave produced using this
method is 500 MHz.
2.
The output frequency is independent of temperature and humidity.
3.
A stable and constant o/p frequency is produced because the breadth of
the resonance curve is small.
4.
It is more efficientthan magnetostriction oscillator.
5.
Using synthetic materials like LiNbO3, BaTiO3 a wide range of
frequencies can be generated at lower cost.
e)
1.
2.
f)
1.
2.
3.
Disadvantages
The cost of Piezoelectric quartz plate is very high.
The cutting and shaping of the piezoelectric crystal is difficult.
Applications
Ultrasonic cleaner
Ultrasonic solder
NDT
Magnetostriction Effect Or Joule Effect
Whenever a ferromagnetic material like nickel is subjected to a static
magnetic field, there is a change of thedimension of the ferromagnetic
material.
Consider that the length of the ferromagnetic material increases due to the
application of magnetic field. If the polarity of the magnetic field is reversed,
the length of the ferromagnetic material decreases. Instead of applying a static
magnetic field, if a variable magnetic field is applied to a ferromagnetic
material, the length of the material continuously changes. During one half
cycle of the magnetic field, the length of the ferromagnetic material increases
and during the other half cycle of magnetic field the length decreases.
When an alternating magnetic field is applied to a ferromagnetic material,
there is a continuous change of the dimension of the material and hence the
material is set into vibration. This phenomenon is known as
magnetostriction method.
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Or
“ When a ferromagnetic rod is subjected to an axial magnetic field, its length
increases and decreases”. This is known as Magnetostriction effect.
If the length of the rod increases it is known as positive magnetostriction effect
and if the length of the rod decreases it is known as negative magnetostriction
effect. This effect is independent of the sign of the field but depends on the
magnitude of the field and nature of the material. This effect is strong in
ferromagnetic materials like iron , cobalt, nickel and their alloys.
It is seen from the fig. that nickel and annealed cobalt exhibit a
simple and regular behavior. A rod made of either of these two metals shows a
decrease in length when exposed to increase in magnetic field. Further, this
phenomenon is reversible. If a magnetic rod say nickel is stretched, the
magnetization of the rod decreases. Compression of the rod along the length
increases the magnetization. Accordingly if a coil is wound around a rod, any
elastic deformation of the rod induces a voltage in the rod.
If a nickel rod is brought into an alternating magnetic field, the
varying magnetization of the rod shortens the rod periodically. An
unmagnetized rod then vibrates at a frequency twice that of a.c field. On the
other hand, if a previously magnetized rod is kept in an externala.c magnetic
field, the change in length of the rod follows the ac field and when the
frequency of both of them is same due to resonance, ultrasonicsare produced.
The frequency of the rod is given by
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1 Y
2l 
Where ‘Y’ is the Young’s modulus of the bar material and ‘ρ’ is its density. Pure
nickel and nickel alloys such as invar and monel metal yield good results.
f 
Magnetostriction Oscillator
The magnetostriction oscillator was discovered by Joule. This method is based
on the principle of magnetostriction.
Principle
“ When a ferromagnetic rod is subjected to an axial magnetic field, its length
increases and decreases”. This is known as Magnetostriction effect.
If the length of the rod increases it is known as positive magnetostriction effect
and if the length of the rod decreases it is known as negative magnetostriction
effect. This effect is independent of the sign of the field but depends on the
magnitude of the field and nature of the material. This effect is strong in
ferromagnetic materials like iron , cobalt, nickel and their alloys.
Construction
Fig. shows a circuit diagram of magnetostriction oscillator.
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A ferromagnetic rod AB is clamped at the centre. Two coils L1 and L2 wound at
its two ends. The coil L2in combination with a suitable capacitor C forms a
resonance circuit and is connected to the collector of a transistor.
A battery is connected for necessary biasing of the transistor. The frequency of
the oscillator is controlled by varying the capacitor. The current in the circuit
is measured by the milliammeter.
Working
1)
The ferromagnetic rod is initially magnetised by placing it in b/w the
poles of permanent magnets Or by surrounding the rod with a secondary coil
carrying a direct current.
2)
When a battery is switched on the resonant circuit L2C sets up
alternating current.
3)
This alternating current flows through the coil L2 produces an
alternating magnetic field along the length of the rod.
4)
Thus the rod starts vibrating due to magnetostriction effect.
5)
The frequency of the resonant circuit is adjusted such that it is equal to
the frequency of the rod and resonance takes place.
6)
At resonance, the rod vibrates with greater amplitude producing
ultrasonic waves.
At resonance
Frequency of the resonant circuit = Frequency of the rod
1
1 Y

2 L2 C 2l 
i.e frequency of ultrasonic wave produced, f 
Where
1 Y
2l 
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l → length of the rod
Y→ Young’s modulus of the rod
ρ→ Density of the material of the rod
7)
The coil L1helps in increasing the amplitude of ultrasonic waves. The
vibration of the rod produces an e.m.f in the coil.
8)
This emf is applied to the base of the transistor which increases the
amplitude of oscillations in coil L2 due to positive feedback.
Advantages
1)
Its construction is simple.
2)
Its cost is low.
3)
At low ultrasonic frequencies, large power out put is possible with out
damaging the resonance circuit.i.e , Using this method, the ultrasonic waves
having frequency up to 300kHz can be produced.
Disadvantages
1)
It cannot generate ultrasonics of frequency above 3×102kHz.
2)
The frequency of oscillations depends greatly on temperature.
3)
When a single rod of ferromagnetic material is used eddy current losses
appear.
4)
Since frequency of vibration depends on the length of the rod, different
ferromagnetic rod has to be used to produce different frequencies.
Applications
Widely used for applications demanding high power like Ultrasonic welding,
cutting and drilling.
Detection of Ultrasonics
a)
Piezo-Electric Detector Method
Ultrasonics can be detected using the principle of piezo electric effect. A pair of
opposite faces of quartz crystal is subjected to the given waves. If alternate
electric charges are developed on the other pair of opposite faces of the crystal
in a perpendicular direction, the waves are ultrasonics. The charges developed
are very small but they can be amplified and detected by suitable devices.
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b)
Thermal Detection
Ultrasonics waves produce alternate compression and
rarefraction while
passing through a gaseous Or liquid medium. The compression of particles
produces heat energy and rarefraction produces the cooling effect. If a
platinum wire is placed in the medium of ultrasonic waves, the change in
resistance of wire w.r.to temperature is observed.
The amount of temp.change is directly proportional to the intensity of
ultrasonic waves.
Construction
In the bridge circuit A & B are fixed standard resistance, C is a variable
resistance and the platinum wire is connected in the fourth arm D of the
bridge. A galvanometer is connected to check the balancing position of the
bridge.
Working
1)
Initially the bridge is kept in balance position.
2)
The platinum wire is moved in the medium containing ultrasonic waves.
3)
If the stationary waves are produced at the nodes the temperature
changes and at antinodes the temperature remains constant.
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4)
Due to the change in temperature the resistance of the wire is changed
which makes the bridge to unbalanced condition.
5)
The change in resistance of the wire w.r.to temperature is detected with
the help of high sensitive micrometer.
6)
This micrometer is calibrated interms of intensity of ultrasonic waves.
c)
Sensitive Flame method
A very sensitive flame( like candle flame) is moved slowly through a medium in
which ultrasonic waves are existing. If the waves are ultrasonics, the flame
flickers at nodes while it remains stationary and undisturbed at anti-nodes.
The flickering at the nodes is due to the compression and rarefraction taking
place very rapidly.
d) Kundt’s tube Method
A Kundt’s tube is a glass tube in which the two ends are covered by two
piston, one is movable and another is fixed.
First lycopodium powder is sprinkled uniformly in the tube. When ultrasonic
waves are passed through the tube, with the help of an adjustable piston
standing waves pattern is obtained. It means that the powder produces heaps
at the nodes and is blown off at the antinodes. This confirm the presence of
ultrasonic waves.
The distance b/w any two nodes is equal to half of the wavelength
ie d=λ/2.
This method however fails as the wavelength of ultrasonics is very small, i.e
less than few mm.
PROPERTIES OF ULTRASONIC WAVES
1)
These are sound waves having frequencies greater than 20kHz.
2)
As the wavelength of ultrasonics is very small(  1.65cm), the energy
associated with ultrasonics is enormous,they have intensity up to 10kW/m2.
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3)
Ultrasonics can penetrate through metals and other materials which are
opaque to electromagnetic waves.
4)
A medium is necessary for the propagation of Ultrasonics.i.e,
Ultrasonics can’t travel through vacuum.
5)
Speed of propagation of ultrasonic waves depends on their frequency.
Larger the frequency, higher the speed of propagation.
6)
Ultrasonic waves can be focused by lenses made from plastic and
metals.
7)
The Ultrasonics can travel through different media with different
velocities.
The velocity of ultrasonics in solid V is given by V =
Where Y is the Young’s modulus and

ρ is the density of the material of solid.
The velocity of Ultrasonics in liquids is given by V=
Where ‘K’ is the bulk modulus and
Y
K

.
ρ
is the density of the liquid.
P
The velocity of Ultrasonic waves in gas is given by V=

Where ‘P’ is the pressure and ρ is the density and  is the ratio of specific
Cp
heats of gases. So that
.
Cv
8)
Ultrasonics can propagate through a medium in different modes. There
are four modes Of propagation.

Ultrasonics can be propagated as longitudinal waves Or compressional
wave in solids and Fluids. The particles of the medium vibrate parallel to the
direction of propagation and this produces alternate condensation and
rarefraction.

They can propagate as transverse waves in solids. The particle of the
medium vibrate perpendicular to the direction of propagation.

Ultrasonics can be propagated as surface waves along the surface of
solids as in the
case of a thick solid block.

They can be propagated as plate waves along a very thin sheet of
materials.
9)
Thermal Effect: When Ultrasonics beam is focused to a sharp point,
heat energy will be produced. When ultrasonics are passed through a liquid ,
its temperature gets increased due to absorption.
10) Stirring Effect: when ultrasonicsare passed through certain low
viscous liquid they get stirred up violently forming emulsions.
11) Cavitation Effect: When ultrasonicsare passed through certain
liquids containing very minute air bubbles, they begins to grow in size. At a
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critical pressure conditions bubbles collapse together releasing a huge
amount of energy. This is known as Cavitation.
This effects is utilized in cleaning, degreasing of components, soldering of
aluminium and its alloy.
12) Like ordinary sound waves Ultrasonic waves get reflected, refracted and
absorbed.
13) Due to small wavelength, the Ultrasonics waves show negligible
diffraction.
14) They can travel over long distance.
Determination of Velocity of Ultrasonic Waves
( Acoustic Grating)
Principle
When Ultrasonic waves propagate in a liquid medium, the stationary waves
are formed. Thi will change the density of the medium and hence change in
refractive index of the liquid. Now the liquid column acts as diffraction grating
and called as acoustic grating.
If a monochromatic light passed through the liquid, diffraction of light takes
place.
Construction
A spectrometer is used for finding the velocity of ultrasonic waves in a
liquid. A glass tank filled with liquid kept on the prism table. Apiezoelectric
crystal is fixedat the bottom of the tank and vibrated by an oscillatory
circuit. S is a monochromatic source.
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Working
1. Initially the Piezo electric crystal is at rest and the monochromatic light
from the source is passed through the liquid.
2. A vertical peak is observed in the telescope. It means that there is no
diffraction.
3. Now the oscillatory circuit is switched ON and the crystal starts to vibrate it
produces Ultrasonic waves which is propagated in to the liquid, forms
stationary waves.
4. Due to alterating compression and rarefraction, the density of the liquid
changes. At the compression ( nodes), the density is maximum and at the
rarefraction( anti nodes), the density is minimum.
5. The regions of greater density is similar to the rulings of grating and the
region of minimum density are similar to transparent slits of grating.
6. Now, if the light is made to pass through the liquid it will get diffracted.
7. The diffraction pattern consists of central maximua and principal maxima
on either side.
Calculation of Velocity
Bragg’s condition for diffraction is
(1)
2d sin   n
Where d
distance between successive nodes Or anti nodes.
  angle of diffraction
n
order of diffraction
λwavelength of light
If ‘λu’ is the wavelength of ultrasonics, then from the fig
λu=2d
(2)
sub (2) in (1)
λusinθ=nλ
n
u 
sin 
Then velocity of the ultrasonics can be calculated using the relation
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v = fnλ
v
fn
sin 
Where ‘f’ is the frequency of ultrasonic waves.
Application OfUltrasonics
Ultrasonicsare widely used in different fields like engineering, industry
chemical and pharmaceutical fields and medical field etc.
Industrial Application
a)
Ultrasonic Welding
When high energetic ultrasonic waves are made to incident on two pieces of
material kept in contact under pressur produces the material melts and hence
create a joint. This process is called cold welding because during welding
stress is induced and no heat energy is evolved. Two portions are joined
together at a very low temperature. Ultrasonic welding is commonly used to
weld plastics and joined for dissimilar materials. The frequency of the range of
20 kHz to 70 kHz. The ultrasonic welding is used for the following fields

The Ultrasonic welding is used for cell phones, consumer electronics,
disposable medical tools, toys etc.

It is used to carry out small welds in malleable metals such as Al,Cu,Ni.

It is used to join any two dissimilar materials.
b)
Ultrasonic Cleaning
The Ultrasonic waves are used for the purpose of cleaning in
Industry . Generally for cleaning , acetone Or the soap solutions is used. In
Ultrasonic cleaning, the materials to be cleaned are taken in an ultrasonic
cleaning both that contains a cleaning solutions such as soap solution and an
ultrasonic generator. The ultrasonic waves produced by the generator are
passed through the cleaning solution. The Ultrasonic waves produce bubbles
due to the cavitation effect whenever they are passing through liquids. When
these gas bubbles explode a very high amount of energy is released. This
energy torns offs dirt Or the contaminants present in the material. This
method is very useful to clean any delicate materials. The jewelers use this
method to clean jewellery.
23
c)
Ultrasonic Soldering
Normally a flux is used in soldering process to remove the contaminants,
grease and oxide films present on the surface. But active metals such as
Aluminium can’t be soldered by this method. The Ultrasonicswaves is used to
solder on aluminium. Soldering is made on aluminium using a special
soldering iron, which vibrates at the frequency of the ultrasonic wave on
aluminium metal removes the oxide layer and then soldering is made on
aluminium without flux
d)
Ultrasonic Drilling
Ultrasonic drilling is a vibratory process used to drill hole in hard materials
like glass, diamond etc.
24
It consists of a thin isolated ferromagnetic needle of high magnetostriction
such as nickel as shown in fig.
A coil is wound on the needle to produce magnetostriction effect. An aqueous
suspension of corborundum powder ( called as slurry), is fed through a tube to
the working area. Nowthe needle vibrator is made to vibrate and the tool
shank is pressed against the work piece. The slurry particles bombard the
work surface at high velocityand remove small pieces of the material. The
repeated action make a hole on the surface.
e)
Non DestructiveTesting- Ultrasonic Flaw Detector
NDT is a method of testing the material without destructing Or damaging the
material. Ultrasonics are used to find any hole, crack Or flaw present in a
material.
Principle
Ultrasonic waves are reflected at the interface b/w two media. Thus whenever
there is a change in a medium, the ultrasonic waves are reflected.
Construction
Figure shows the block diagram of Ultrasonic Flaw detector. It consists of a
pulse generator to generate electric pulses. A Piezoelectric crystal is used to
produce and detect ultrasonic waves. It is placed on the surface without any
air gap. An amplifier amplifies the weak signal. A CRO is used to display the
electric pulses.
25
Working
1.
The Pulse generator generate electric pulses and applied it to the
Piezoelectric crystal . The same pulse is recorded in CRO as pulse reference.
2.
The crystal generate Ultrasonic waves and transmit into the specimen.
3.
It is reflected back and detected by the transducer which convert this
into electric signals.
4.
The electric signal get amplified and fed into the CRO.
The time difference b/w the two peaks is used to measure the velocity of the
Ultrasonic wave.
2d
V 
t
Where ‘t’ is the time difference b/w the transmitted and reflected signal.
5.
If there is any discontinuity like a flaw in the specimen, then another
echo is seen b/w the transmitted signal and the signal reflected from the
bottom surface. The time difference b/w the transmitted signal and the
reflected signal from the flaw is used to find the depth of flaw using the
relation.
d1 
vt
2
Where d1 is the depth of flaw, ‘v’ is the velocity of the ultrasonic wave in the
specimen and ‘t’ is the time taken.
Pulse A
Transmitted signal
Pulse C
Reflected signal from the bottom surface
Pulse D
Signal due to flaw
6.
Absence of the pulse B, indicates that there is no flaw in the material.
Advantages
1.
Defects at any depth in specimen can be detected.
2.
Minute flaws can be detected.
3.
Recent developments in software permits recording of data.
4.
It is one of the cheapest method.
5.
Ultrasonicsequipmentsis compact and portable.
6.
Permanents records can be maintained.
7.
The ultrasonic test can be made in a small specimen.
Disadvantages
1.
The skilled operators are needed to interpret the result.
2.
Irregular shape and rough specimen cannot be studied.
3.
Flaw estimation requires some standard specimen.
26
2) Marine Applications
a) Depth of Sea Or Echo Sounder
The Ultrasonic wave exhibit very feeble diffraction effect and they are not
absorbed by the sea water. On the basis of this property ultrasonic wave can
be transmitted through water for a long distance. Consider a piezoelectric
tranducer is used to produce the ultrasonic waves and it transmitted towards
the bed of sea water. The ultrasonic wave reflected from the bed of the sea
water is collected and time taken for the to and fro motion is noted. Then by
knowing the velocity of ultrasonic wave in sea water, the depth of sea water is
determined.
vt
Depth of the sea= 2
Where ‘v’ is the velocity of the ultrasonic wave in sea water and ‘t’ is the time
taken for the to and fro motion.
b) SONAR( Sound Navigation And Ranging)
Ultrasonic waves of high frequency are used to find the distance and direction
of submarine, depth of sea, depth of rocks and the shoals of fish in the sea ,
ice bergs etc. Hence the device used for is named as SONAR which stands for
Sound Navigation And Ranging.
Principle
The device is operated on the principle of echo sounding technique. The
principle is
“ When Ultrasonic waves are transmitted through water, it is reflected by the
object in the water in the form of echo signal. Thus by knowing the change in
27
frequency due o Doppler effect, the velocity and hence direction of the object
can be determined”
Construction
The block diagram of sonar is as shown in fig. It consists of a timing section
which triggers the pulse generator to generate electric pulses. Two piezo
electric crystals, one act as transmitter and the other act as receiver are used.
A CRO is connected to receiver as well as pulse generator. The timing section
is also connected to the CRO for reference of the timing at which the pulse is
transmitted.
Velocity of the beam v 
2d
, where
t
d
depth of the sea
ttime delay between sending out and receiving back of ultrasonic beam in
sonar.
Working
1. Timing section triggers the pulse generator to generate electric signals.
2. This electric signal is applied to Piezo crystal to generate ultrasonic waves
and transmit on to the object. Here the Piezo electric crystal act as
transmitter.
3. The time at which the pulse transmitted is recorded in CRO.
4. The waves reflected by the object is detected by another crystal and
converted into electrical signal. Here the Piezo electric crystal act as
receiver.
5. This electrical signal is fed to the CRO. From the time interval b/w the
pulse transmitted and the pulse received, the position, distance and the
direction of the moving object can be determined.
28
6. Velocity of the ultrasonic in the sea water v 
K

,where K is the bulk
modulus and ‘ρ’ is the density of the sea water.
In Medicine
Ultrasonic waves are more free from harmful effects and they will not
produce any discomfort and distress to the patient( unlike x-rays). So
they are used for both diagnosis and therapy
1. Diagnosis
Diagnosis is mostly based on ultrasonic scanning Orimagings.
Ultrasonic waves are transmitted through our body and they are
reflected from the boundaries of organs due to difference in density.
The echo pulses are received ,amplified and fed to the screen of a CRO.
We can see the clear pictures of our internal organs like
heart,liver,lungs, kidney, intestine , bladder etc. This Ultrasonic echo
test is used for
a) The detection of heart complaint, brain tumour, cancer etc.
b) For pregnancy test.
c) The Doppler effect of ultrasonics is used to detect the motion of
featal heart.
d) For providing details about the size, location and displacement of a
structure with the help of Doppler effect without any surgery.
29
2. Therapy
a) Used for the treatment of muscle pains and rheumatic pains.
When Ultrasonic waves are transmitted through the muscles,
tissues begins to vibrate in unison with the waves and this will
producing a massaging effect.
b) A high pressure Ultrasonic beam is used to crush up kidney
stones.
c) Acoustic Surgery: In laser guided surgery ultrasonic pulses are
focused to a sharp point where intense heat energy developed
destroys the timorous cells.
d) Ultrasonic are used to stop the internal bleeding.
e) Ultrasonic scrubber together with a water get is used to remove
plaque from teeth.
f) Ultrasonic beam is used for bloodless surgery.
g) They are used for the treatment of neuropatients.
h) Ultrasonic beam is used to measure the distance in eye, like
lens thickness, depth of cornea from lens, distance to the retina,
thickness of vitreous humour etc.
a) Sonogram
Sonogram, also known as an ultrasound, is a computerized
picture taken by proceeding ultrasound echoes from organs and
other interior parts of the body.
The Ultrasound Machine
A basic ultrasound machine has the following parts:

waves
Transducer probe - probe that sends and receives the sound
30
Central processing unit (CPU) - computer that does all of the
calculations and contains the electrical power supplies for itself and the
transducer probe

Transducer pulse controls - changes the amplitude, frequency
and duration of the pulses emitted from the transducer probe

Display - displays the image from the ultrasound data processed
by the CPU

Keyboard/cursor - inputs data and takes measurements from the
display

Disk storage device (hard, floppy, CD) - stores the acquired
images

Printer - prints the image from the displayed data

The transducer probe is the main part of the ultrasound machine. The
transducer probe makes the sound waves and receives the echoes. It is,
so to speak, the mouth and ears of the ultrasound machine. The
transducer probe generates and receives sound waves using a principle
called the piezoelectric (pressure electricity) effect, which was
discovered by Pierre and Jacques Curie in 1880. In the probe, there are
one or more quartz crystals called piezoelectric crystals. When an
electric current is applied to these crystals, they change shape rapidly.
The rapid shape changes, or vibrations, of the crystals produce sound
waves that travel outward. Conversely, when sound or pressure waves
hit the crystals, they emit electrical currents. Therefore, the same
crystals can be used to send and receive sound waves. The probe also
has a sound absorbing substance to eliminate back reflections from the
probe itself, and an acoustic lens to help focus the emitted sound waves.
Transducer probes come in many shapes and sizes, as shown in the
photo above. The shape of the probe determines its field of view, and the
frequency of emitted sound waves determines how deep the sound
waves penetrate and the resolution of the image. Transducer probes
may contain one or more crystal elements; in multiple-element probes,
each crystal has its own circuit. Multiple-element probes have the
advantage that the ultrasounc beam can be "steered" by changing the
timing in which each element gets pulsed; steering the beam is
especially important for cardiac ultrasound (see Basic Principles of
Ultrasound for details on transducers). In addition to probes that can be
moved across the surface of the body, some probes are designed to be
inserted through various openings of the body (vagina, rectum,
esophagus) so that they can get closer to the organ being examined
(uterus, prostate gland, stomach); getting closer to the organ can allow
for more detailed views.
31
The parts of an ultrasound machine
The CPU is the brain of the ultrasound machine. The CPU is basically a
computer that contains the microprocessor, memory, amplifiers and
power supplies for the microprocessor and transducer probe. The CPU
sends electrical currents to the transducer probe to emit sound waves,
and also receives the electrical pulses from the probes that were created
from the returning echoes. The CPU does all of the calculations involved
in processing the data. Once the raw data are processed, the CPU forms
the image on the monitor. The CPU can also store the processed data
and/or image on disk.
The transducer pulse controls allow the operator, called the
ultrasonographer, to set and change the frequency and duration of the
ultrasound pulses, as well as the scan mode of the machine. The
commands from the operator are translated into changing electric
currents that are applied to the piezoelectric crystals in the transducer
probe.
32
b) Blood Flow Velocimeter ( Blood Flow Measurement)
The continuous Doppler shift is used to find out the speed of the blood
in the veins and arteries. Consider that an ultrasonic transducer is
positioned on the skin at an angle of ‘θ’ to the blood vessel. If the
ultrasonic wave is passed through the skin, it get reflected back by the
moving object like blood and the stationary object like blood vessel.
The blood is moving with a velocity of ‘v’ and the transducer is inclined
at an angle ‘θ’. Therefore, the blood has a component ‘vcosθ’ along the
beam direction. So, the Doppler shift produced by the movement of
blood is
2 fv cos 
f 
c
Where ‘v’ is the speed of the blood, ‘c’ is the speed of the ultrasonic
wave through the human body, ‘f’ is the frequency of the transducer,’θ’
is the angle of inclination of the probe with blood vessel and ‘∆f’ is the
Doppler shifted frequency.
This method has some advantages. They are (i) there is no need of surgical
penetration of the vessel and (ii) continuous reading can be made with out
any risk or discomfort. Using this method direction of blood flow is not
identified. But by using a colour Doppler flowmeter, one can identify the
direction of the flow.
33
Other Applications
f)
Sterilization
Unicellular organisms can be destroyed when exposed to ultrasonic
waves. Ultrasonicsare used to sterilize water, milk etc.
g)
Destruction of Lower Life
Applying very high intense beam of ultrasonics, very small animals like
frog, fish, rat etc. can be killed Or injured.
h)
Ultrasonic Signaling
Ultrasonic waves are concentrated into narrow beam and can be directed
to distant places due to their high frequency. Hence they are used for
signaling in a particular direction.
Disadvantages of Ultrasonics
i)
Ultrasonic devices are very expensive.
ii) The Ultrasonic devices are complex in design
iii) In medical examination of human using ultrasound, tissues Or
water absorb ultrasound energy, which increases their temperature
locally.
iv) During passage of ultrasonics through liquids, dissolved gases may
come out of it due to cavitation.
v) Bats,dogs and some other animals are capable of perceiving ultrasonic
waves. Hence if ultrasonic waves are sent around in open, it causes rest
lessness amongst some animals and birds.
**********************************************************
Reference
1.
2.
3.
4.
5.
6.
7.
Engineering Physics by A. Marikani
Engineering Physics by Randehir Singh
Engineering Physics by K. Rajagopal
Engineering Physics By TessyIssac
A text book of Engineering Physics – M.N Avadhanulu
Engineering Physics -1 - S.Gopinath
Engineering Physics- Jacob Philip
34
MODULE-5
CHAPTER-3
SPECTROSCOPY
Introduction
Spectroscopy is defined as branch of physics which deals with interaction b/w matter
and radiation. It can also be defined as science of measuring emission and absorption of
different wavelengths of electromagnetic radiation. When a polychromatic light is made
to incident on certain medium, it scatters light in various directions. Depending on the
electronic structure of atoms, certain specific wavelength may be absorbed by the
substance from light incident on it. Thus these wavelengths will be missing in the
scattered light. If light coming out from medium is put on a screen the pattern of various
wavelengths formed on the screen is called spectrum. Spectroscopy is very useful in
determining the structure of various molecules and in various medical applications and
in many other applications.
Energy is radiated as spectral lines when an electron, atom Or molecule makes a
transition b/w energy states. The electromagnetic waves are travelling with space with
velocity, c =3x 108m/s. A wave is characterized with its wavelength  and frequency 
and they are related through the equation
c=  . Electromagnetic radiation is also represented in terms other parameter called

wave number  .

1
 = , unit is cm-1 or m-1

Wave number is defined as number of wave contained in one meter length.
RAYLEIGH SCATTERINGOr COHERENT SCATTERING
Rayleigh permitted monochromatic light to fall on a sample of
transparent material. The size of thesample is much smaller than the wavelength of
light. The light is scattered in all directions. He found that there is no change in
frequency or wavelength during scattering. When blue light is used for irradiation, he
obtained same blue light after scattering. Such a scattering of light radiation by a
material in which there is no change in frequency is called Rayleigh’s scattering.
35
Here scattering is due to the elastic collision between the
incident photons and the molecules of the scatterer. During this elastic collision
there is no exchange of energy between the photons and the molecules of the
scatterer. The photon is simply deflected by the molecule without any exchange of
energy. So this scattering is called coherent scattering. Hence the spectrum of
scattered radiations is same as that of the incident radiation. This unmodified line has
the same frequency as that of the incident line and this parent line is referred as
Rayleigh’s line.
“ The scattering of light radiation by a material in which there is no change in
frequency is called Rayleigh’s scattering ”
(a) Rayleigh’s scattering Equation: Rayleigh’s scattering takes place only when the
scattering molecule is much smaller than the wavelength of the incident photon.
Rayleigh derived an expression for the intensity of radiation as,
I0
- intensity of incident radiation
r
- Radius of the scattering particle of the sample
n
- Refractive index of the material
d
- Distance between scattering sphere and the observing point
Since d and n remain constants, it is found that the intensity of scattered radiations
I α r6
and I α
1
The most important theorem namely, the intensity is inversely proportional to the fourth
power of wavelength of light used is called Rayleigh’s scattering equation or theorem
I
1
4
.Thus according to Rayleigh’s theorem, smaller the wavelength of light higher will
be the scattering.
36
(b) Colour of Sky and Sea
Colour of sky is due to the Rayleigh’s scattering of white light with gas molecules and
other particles present in the atmosphere. Atmosphere mainly consists neutral atoms of
gases like Nitrogen (78%), Oxygen (21%) etc. and other particles like dust, ashes,
pollen, salt etc. The radii of these particles (size) are much smaller than the wavelength
of different components of sunlight. (Sunlight contains VIBGYOR, each colour has its
own different wavelength). When sunlight is incident on these particles, it gets reflected
and scattered. By Rayleigh’s theorem the intensity of scattered light is inversely
proportional to the fourth power of the wavelength of light. This shows that the smaller
wavelength part of the light is effectively and strongly scattered than the higher
wavelength part. Hence violet and blue are more scattered than red. When the sun is
directly above, light rays have to travel a shorter distance to reach the observer. Blue
colour is scattered in all directions and spreads around. So when we look on the sky in
any direction, blue light reaches in our eyes from anywhere and sky appears blue in a
sunny day. At noon on a sunny day, when sun is overhead, light falls directly and travels
only shorter distance to reach earth, so sun appears as white. When we observe close to
the horizon, the sky appears paler, in colour. This is because the scattered blue light is
again scattered away and a less amount of blue light is alone reaching the earth. This
makes the sky paler in colour.
Colour of sea and ocean can also be explained in a same manner. When sunlight is
incident on sea water, blue light gets more strongly scattered from the water molecules
as per Rayleigh’s scattering. Blue light is scattered out in all directions and spreads all
around. So sea or ocean appears as blue in colour on a sunny day.
(C) Red Colour of Sun During Sunset or Sunrise
It is also explained by Rayleigh’s scattering. Sun is low when the
sun begins to set. So light has to travel longer distance through the atmosphere before
reaching in our eyes. Shorter wavelength part of the sunlight like violet and blue are
more scattered out than the longer wavelength part like red. White light without blue is
almost yellowish red. Red light travels through the atmosphere and reaches in our eye
without any loss in energy. So the setting sun appears yellow and orange. When more
and lower wavelength part like green is also scattered out the remaining white light is
dominant with red. As a result sun appears deep red during sunset. The same explanation
is valid to the red colour of sun at sun rise. The sky also undergoes such a colour
variation during sunrise and sunset. Its colour changes to yellow, pink, orange and
37
finally red due to Rayleigh’s scattering. But presence of clouds may disturb the colour
pattern.
In a sunny day clouds appear white or achromatic gray in contrast with
the blue colour of the sky. This is because size of the water particles which constitute
clouds is larger than the wavelength of component colours of sunlight. Hence reflection
and scattering are taking place. But the scattering is never Rayleigh’s scattering since the
size of particles is larger. This type of scattering is independent of wavelength. Hence
the cloud appears white or achromatic gray.
In space sky is dark since there is no atmospheric scattering. Sun
appears very bright. This can be observed from an aero plane at very high altitudes.
RAMAN SCATTERING Or INCOHERENT SCATTERING
When monochromatic radiation is allowed to incident on
transparent solid or dust free liquids and gases, a fraction of the incident radiation is
scattered. Most of the scattered radiations have the same frequency as the incident one.
However, a few are scattered with a difference in frequency. This phenomenon, first
observed by Sir C.V. Raman in 1928, is known as Raman scattering. The lines having
frequencies on the low and high frequency side of the exciting line (Rayleigh line) are
called Stokes and anti- stokes lines respectively. These weak lines of modified
frequencies are referred to as the Raman lines or Raman spectrum and the frequency
shift from the exciting line is called Raman shift. This phenomenon is also known as
Raman Effect. He won the Nobel Prize in Physics in 1930 for this discovery.
Discovery of Raman Effect
Raman was studying the scattering of light with different transparent substances in solid,
liquid Or gaseous state. He used sunlight for molecular scattering. Using the blue-violet
filter coupled with Uranium plate Raman selected Blue ray as the monochromatic
radiation. This light is passed through a transparent organic liquid like benzene, toluene,
carbon disulphideetc contained in a round bottom flask. The scattered radiations from
the molecules of the liquid were observed through a spectroscope in a perpendicular
direction. To his surprise Raman found that the scattered radiations contained other
38
frequencies also like green in addition to blue line. i.e, Scattered radiations contained
other frequencies in addition to original frequency.These lines are strongly polarized.
At first he thought that these additional modified lines are due to feeble florescence.
But florescence lines are never polarized. Hence he confirmed that this is a special
type of modified scattering.
RAMAN EFFECT
When monochromatic light is passed through certain transparent substances in solid,
liquid or gaseous state, the scattered radiations contain other frequencies in addition to
the original incident frequency. Such scattering of light by a substance producing a
change in frequency or wavelength is called Raman Effect or Raman scattering or
incoherent scattering.
(a) Raman Spectrum
Most part of the incident radiations are not affected during scattering.
i.e. there is no change in frequency during scattering (Rayleigh scattering). Hence we get
the original incident line called unmodified line or Rayleigh line in the scattered
radiations. But a small part of the incident radiation has undergone a change in
frequency or wavelength during scattering. Hence we get modified spectral lines in
addition to the parent line. A spectrum consisting of original parent line and modified
lines is called Raman spectrum. Modified lines with frequencies other than that of the
incident line are called Raman lines. Raman lines are distributed symmetrically on either
side of the unmodified parent line. Raman lines consist of two types of modified linesStoke’s lines and antistoke’s lines. Modified Raman lines with frequency smaller than
that of the parent line are called Stoke’s lines (Wavelength will be larger). Modified
Raman lines with frequencies greater than that of the parent line are called antistoke’s
lines (Wavelength will be smaller). Stokes and antistokes lines are symmetrically placed
about the Rayleigh line. But the stokes are more intense than antistokes,
The difference in frequency between a Raman line and the parent
line (Rayleigh line) is called Roman shfi (∆  ) or Raman frequency.
39
If  0 be the frequency of incident radiations (parent line) and 1 is
the frequency of the scattered modified lines or Raman lines.
Raman shift ,    0  1 . Raman shift  is positive for antistoke’s
lines and it is negative for stoke’s lines. Raman shift does not depend on the frequency
of incident radiations and it depends only on the characteristics of the scattering
substance. Hence the number of Raman lines and Raman shift are the characteristics of
the scatterer.Raman shift in terms of wavenumber is given as ,
   0  1 
1
1

1
2
, it is always expressed in cm-1 or m-1.
(b) Characteristic properties of Raman lines
Some of the important characteristics of Raman lines are given below.
1) Raman lines are symmetrically situated about the original parent line (Stoke’s
and anitstoke’s lines are symmetrically placed on either side of the parent line).
2) When temperature increases the individual separation of each Raman line from
the parent line decreases.
3) The intensity of Stoke’s lines is always higher than that of antistoke’s lines.
4) Raman shift ∆ν is generally within far and near infrared regions of the
spectrum. i.e Raman frequencies are generally identical with infrared and
vibrational frequencies.
40
5) Frequency difference between the parent unmodified line and modified line
represents the frequency of the absorption band of the material.
Relative intensities of stoke’s and antistokes’ lines
From the theoretical explanation of Raman effect based on
quantum theory it is clear that the stokes’ and antistokes’ lines are produced
according as the molecule absorbs energy from the molecule Or give energy to the
molecule. This can happen according as the molecule is in the ground state Or in
the excited state The intensity of any line is proportional to the number of
molecules giving rise to that line. The no. of molecules in any energy states
decreases rapidly with increase of energy. Hence there will be large no. of
molecules in the ground state than in any excited state. Correspondingly the
stokes, lines which are produced by the ground state Or low enery state molecules
will be much more intense than the corresponding antistoke’s lines.
Intensity of stokes lines
Intensity of antistokes’ lines
= No. of molecules in the ground state
No. of molecules in the excited state
(d) Quantum Theory of Raman Effect
Inspired from the success of Compton scattering effect with X-rays and Einstein’s
photoelectric effect with light rays, Raman explained Raman effect on the basis of
quantum theory of radiations. Raman effect is due to the interaction between the
incident photons and a molecule of the scatterer. Raman lines are produced during
the inelastic collision between photons and molecules.
Consider a molecule with intrinsic energy E1 with mass
‘m’ moving with a velocity v1, colliding with a photon of energy h 1 , where 1 is
the frequency of incident photon (incident radiation). During this collision there is
an exchange of energy between photons and the molecule. As a result, the
intrinsic energy of the molecule changes to E2and it moves with a velocity v2 after
collision. Similarly the energy of photon is changed to h  2 after collision, where
41
 2 is the frequency of the scattered photons (scattered radiations). By the law of
conservation of energy,
Total energy before collision = Total energy after collision
E1 
1
1
mv12  h1  E 2  mv22  h 2
2
2
But the change in velocity of the molecule during collision is negligible
i.e.v1=v2
E1  h1  E2  h2
h2  h1  E1  E2
E  E2
2  1  1
 (1)
h
The difference in frequency b/w scattered radiation and incident radiation is called
Raman shift
i.e, Raman shift    2  1
Raman shift in terms of wave number is
   2  1 
1
2

1
1
Three different cases may take place:
Case 1: E1 = E2,   0 or 1 =  2
This reveals that there is no change in frequency during molecular
scattering. Hence we get the original parent line in the spectrum. This unmodified
line is called Rayleigh line. In this case molecule simply deflects the incident
photon without any exchange of energy. Hence the collision is purely elastic and
this scattering corresponds to Rayleigh’s scattering or coherent scattering as per
classical theory.
Case 2: E1> E2,  2 > 1 or ∆  is Positive and it represents antistoke’slines
In this case frequency of scattered photons is greater than the frequency of incident
photons. This reveals that the molecule was initially in an excited state (higher
energy state). It supplies a part of its intrinsic energy to the colliding photons. Hence the
photons gain the additional energy and scattered with higher frequency.
Case 3: E1< E2, or  2 < 1 or ∆  is negative and it represents stoke’s lines
42
Here a molecule is at a lower energy state. It absorbs a part of energy
from the incident photons and as a result the scattered photon moves with lower
energy. The scattered radiation has a lower frequency and it corresponds to
Stoke’s lines.
But the change in intrinsic energy of the molecules must obey the quantum
conditions. i.e, Energy difference must be quantized Or in other words energy
difference must be an integral multiple of smallest quantum of energy.
E1 - E2 = nh C  (2)
Where n=1,2,3….etc, and  C = the characteristic frequency of the molecule.
In the simplest case n=1
Eq(1) E1 - E2 = h  C
C 
E1  E 2
h
Comparing eq(1) and (2)
 2 - 1 =  C
 2 = 1 +  C
 2 = 1 ±  C
This equation shows that the frequency difference ( 1 -  2 ) between the incident
and scattered photon corresponds to the characteristic frequency  C of the
molecule.
43
ν = 0,1,2,3 etc represents different vibrational energy levels of the
molecule at ground electronic state. When the radiation is incident on the
molecule in interaction takes place between the incident photon and the ground
state molecule of the scatterer. Consider a photon of energy hν0 incident a
molecule in the ground state. As a result of the interaction the molecule makes a
transition from the ground state to the virtual state (dotted line represent the
virtual state and this state is not a stationary state). When it returns to the original
ground state a radiation of energy hν0 is emitted. There is no change in frequency
during this transition and hence the scattered radiation has the same frequency as
that of the incident radiations. This corresponds to the unmodified line (Rayleigh
line). The photon is just deviated by the molecule.
If the molecule returns to the higher frequency energy state
(ν = 1) of the ground state, Stoke’s lines are obtained. If molecules are returned to
the lower energy state (ν = 0) of the ground state antistoke’s lines are observed.
Stokes lines are originating from the lower energy state (ν = 0) and antistoke’s
lines are originating from the higher energy state (ν = 1). Antistoke’s lines are less
intense or weaker since they are originating from higher state.
Experimental study of Raman Effect and Raman Spectrum
The basic arrangement for obtaining and observing Raman spectrum is as shown below.
T is a Raman tube in which the liquid is taken for investigation. Raman tube is
made of glass with diameter 2cms and length between 10 to 25cms. One end of the
Raman tube is drawn into a horn shaped part H and its outside is completely darkened to
44
provide a fine and suitable background. The other end of the tube is closed with an
optically plane glass plate. A window W is provided at this end so that the scattered
radiations can be emerging through it. Raman tube is surrounded with a water jacket J
through which cold water is circulating in order to avoid the excess heating of the liquid.
S is a mercury arc lamp arranged nearer to the tube which produces very high intense
beam of light. F is a filter placed in between the source and the tube so that it filters and
permits only highly monochromatic beam to pass through the liquid. Semi cylindrical
polished aluminum reflector R enhances the intensity of incident light.
A convex lens L arranged in front of the window focuses and directs the
scattered radiations upon the slit of the spectroscope. Usually monochromatic blue beam
(4358 A0) is passed through the experimental liquid. The scattered radiations in
perpendicular direction are observed through the spectroscope arranged in front of the
Raman apparatus as in figure. After final adjustments enough exposure time is given so
that clear and well defined Raman spectrum is photographed to a photo plate.
Applications of Raman Effect
Raman spectra were obtained for almost all substances in solid, liquid or
gaseous state. Raman spectrum gives an insight into the structure of molecule of a
substance. Raman effect is very important because of its wide applications.
(1) Analysis of molecular structure: The most important application of Raman
spectrum is in the analysis of molecular structure. Observing a number of Raman
lines, their frequency, intensity and polarization, structure of the molecular
scatterer can be easily estimated. Raman lines depend on the number of atoms in
the molecule, nature of vibrations of the molecule, mass of an atom, nature and
strength of chemical bonds etc...
(2) In physical chemistry: Electrolytic dissociation, hydrolysis, transition from
crystalline to amorphous state etc…have been studied with the help of Raman
spectrum.
a) Raman lines are broad and diffused for amorphous materials while they are
fine and sharp for crystalline state.
b) Intensity of Raman lines predicts the number and nature of the product during
dissociation. So we can decide whether the dissociation is complete or partial.
45
c) Degree of hydrolysis of a salt can be determined by measuring the relative
intensities of Raman lines.
(3) In organic chemistry: Raman spectrum explains clearly the molecular structure of
organic compounds, because each compound has its own characteristic frequency.
Raman spectrum gives information about
a) Classification of various compounds
b) Structure of simple compounds
c) Isomers
d) Impurities in dyes etc…
(4) In polymer chemistry: Raman spectrum of polymers exhibits the properties of
both liquid and crystal simultaneously. This is because polymers have both
amorphous and crystalline regions.
(5) Analysis of mixtures: Raman spectroscopy is successfully used for the easy, rapid
and accurate analysis of mixtures because Raman spectra are simple and height of
Raman lines are directly proportional to the concentrations.
(6) In crystallography: In solid state physics Raman spectroscopy is used to
characterize the materials, measure the temperature and crystallographic
orientation. Raman spectra analysis is utilized to understand macromolecular
orientation in crystal lattices, liquid crystals, or polymer samples. It is also used to
explain specific heat capacities of solids, brilliance of metals etc...
(7) In plasma studies: Raman spectrum is used to study the nature of plasma
diffusion, recombination, energy transfer etc…It can be used as tool to detect high
frequency Plasmons, magnons and electronic excitions.
(8) In combustion diagnostics field: it is used to detect major species and temperature
distribution inside a combustor and in flames.
*************************
REFERENCES:
1. ENGINEERING PHYSICS
2. ADVANNCED PHYSICS
FOR ENGINEERS
: PROF.M.T.ATMAJAN ,S CHAND PUBLICATIONS
: Dr. M.C. SANTHOSH KUMAR
3. MODERN PHYSICS
: S.L.KAKANI , SHUBHRA KAKANI
4. MODERN PHYSICS
: G. ARUL DAS, P. RAJAGOPAL
5. MODERN ENGINEERING PHYSICS : VASUDEVA
46
MODULE-4
CHAPTER-3
ACOUSTICS
Introduction
Acoustics is a branch of sound which deals with the origin,propagation
and reverberation of sound in a room or a hall and it plays an important role in the
modern architectural engineering.The acoustic properties of building were studied
scientifically by the Physics Professor W.C Sabine. He made it clear that
reverberation is the main factor which determines the quality of sound in an
auditorium Or a hall.W.C Sabine has made so many innovations to improve the
quality of sound and hence he is considered to be the founder and pioneer of the
present acoustic engineering.
a) Intensity of Sound
Intensity of sound is the amount of energy transported by the
sound waves per second per unit area of cross section normal to the
direction of propagation.
Q
I
AT
where, Q  Amountofsoundenergyflowing
i.e A  Area
T  Time
If , A  1m 2 , T  1s, I  Q
The intensity is a physical quantity which depends upon the factor like
amplitude ‘a’, frequency ‘f’ and velocity ‘v’ of sound together with density ‘ρ’
of the medium.
i.e I  2 2 a 2 f 2 v
I  E V
I
 2 2 f 2 a 2 
V
The unit of intensity is w/m2 (Watt/m2)
E
47
The intensity of faintest sound that can be heard by a normal human
ear is 10-12W/m2.It is called threshold intensity. If the intensity is less
than this value the our ear cannot here the sound.
b) Loudness and Unit of Loudness
Loudness is the degree of sensation produced on ear. Thus loudness varies
from one listener to another. The loudness depend upon intensity and also
upon sensitiveness of the ear.
Loudness is the characteristics of sound by which we can distinguish
two sounds of same frequency.
Loudness is proportional to logarithm of intensity of sound.
log10I
L=Klog10I
L
Let I0 and I1 be the intensities of two sounds with same frequency and L0
and L1 be the corresponding values of Loudness. Then,
L0
log10I0
L0=Klog10I0
L1=Klog10I1
Where K is a constant of proportionality
“ The difference in loudness L is termed as the intensity level”
I0 is taken as reference intensity and its value is I0=10-12W/m2. This is the intensity
of sound that can be heard at a frequency of 1000Hz. This is taken as threshold of
audibility of normal human ear.
c) BEL(B)
Bel is the unit of loudness Or intensity level. This unit is named as Bel in
the memory of Alexander Graham Bell the inventor of telephone.
I 
Loudness Or intensity level, L  log 10  1  Bel
 I0 
d) Decibel(dB)
Bel is a large unit . Hence a small unit called decibel is used as standard.
1dB=1/10 Bel
Loudness Or intensity level in terms of dB is defined as
48
I 
L  10 log 10  1  dB
 I0 
Absorption And Absorption Coefficient
When sound is produced continuously in a hall from a source, sound energy spread
every where in the hall. When this sound is incident on a surface , it is partially
absorbed, partially transmitted and the remaining part reflected from it. Thus the
walls , ceiling, floor , curtains, furnitures and all other materials kept in the hall
absorb a part of sound energy. Another part of this energy is transmitted and hence
escaped through open windows, open doors, open cavities , ventilators etc. Another
part of energy is reflected from the surface of walls, furnitures and other materials
present in the hall. Thus there is a loss of sound due to reflection, absorption and
transmission. After a few second an equilibrium condition is reached between the
production of sound energy from the source and the loss of sound energy by
different methods. At this equilibrium condition the sound energy
received/second/unit area of listener’s ear attains a steady average value .
Energy is conserved.
ie, E= A+T+R
1=A/E + T/E + R/E
The property of a surface by which the incident sound energy is converted into
other forms of energy is called absorption. The amount of energy absorbed by a
material depends on its surface and its nature. Hence energy absorbed by different
materials will be different.
defined as the ratio of the amount of sound energy absorbed by the surface to the
total amount of sound energy incident on it.
Absorption Coefficient
=Amount of sound energy absorbed by the surface
Total amount of sound energy incident on it
It has no unit it depends on nature of the surface and wavelength of sound waves
incident on it and area of surface.
t( transmission Coefficient) = T/E =Energy transmitted per second
Energy incident per second
R( reflection coefficient) = R/E
= Energy reflected per second
Energy incident per second
A surface is said to be perfect absorber if a=1.(ie, t=r=0) for that surface. Such a
surface is also called open window . The absorption coefficient of open window is
unity.
49
Since an open window absorbs whole amount of sound energy incident on it, open
window is taken as the reference and the absorption coefficient of surface of any
material is represented relative to that of open window.
Thus Absorption Coefficient of a material is defined as the ratio of sound energy
absorbed by an area of its surface to the amount of sound energy absorbed by the
same area of open window.
The unit of absorption of sound energy is called Sabine. One sabine is the amount
of sound energy absorbed by one square foot of an open window in F.P.S. In S.I, the
unit is 1m2 Sabine, which is the amount of sound energy absorbed by one square
meter of an open window.
For unit area of any surface, absorption coefficient is expressed in terms of
equivalent area of open window. If ‘S’ is the total area of a surface and ‘ ’ is
theabsorption coefficient, the equivalent absorbing area ‘A’ is given by
A= S
For example for plaster is 0.05. hen 100m2 of plaster has an equivalent surface
area A=0.05×100=5m2. i.e an 100m2 ofplaster absorb same amount of energy
absorbed by 5m2 of an open window.
Let a room contains different materials with surface areas S1,S2,S3 etc. and
absorption coefficient
1,
2 , 3etc.
Total amount of sound energy absorbed=
1S1+ 2S2+ 3S3+ …………….
Total surface area of the material= S1+S2+S3+……..
Average value of absorption coefficient=
S1+S2+S3+……..
1S1+ 2S2+ 3S3+ …………….
iSi
=
∑Si
=A
S
Where total amount of energy absorbed A=
iSi
50
And Total surface area S =∑Si
Reflection Of Sound
Sound waves get reflected from the surface of materials in a hall and they obey
laws of reflection. Reflection of sound waves in a hall Or in a closed space will
produce echo and reverberation. Both can produce unpleasant effect in an
auditorium.
a) Reverberation
The sensation of hearing produced by a sound is retained within the ear for a
period of 1/10 second. This peculiarity is known as persistence of hearing. If
another sound reaches the ear with in this period, simultaneous hearing is
experienced. Such a continuous and rolling sound is known as Reverberation.
Or
Sound produced in a hall suffers multiple reflections from the walls, ceiling,
floor, furniture and other materials. Hence a listener hears a series of reflected
sound waves in an auditorium in addition to the original sound directly from
the source. So the sound appears to persist for a long time even after the
source has stopped the production of sound. The persistence of sound in a
hall due to the multiple reflections even after the source has cut off the
production of sound is called reverberation.
Or
The listener receives a series of sound of diminishing intensity is known as
reverberation.
Reasons for Reverberation
51
1) Intensity of sound decreases not abruptly , but exponentially. So, it will
take a longer period for the intensity of sound to fall to zero value.
2) Due to multiple reflections from walls, ceilings,floor and other materials in
the hall reverberation takes place and hence the sound remains in the hall
for a long time.
3) Various sound reaching at a point in the hall may not be in the same
phase. This causes interference in a constructive and destructive manner.
As a result there is a reinforcement Or destruction of sound.
Reverberation Time & its Significance
Professor Sabine measured the intensity of sound in a hall with time. If a
graph is plotted b/w intensity and time as shown in fig. , the intensity
grows to a maximum value, and when the sound is stopped it decays to
zero in an exponential manner ( i.e. first rapidly and then slowly). Clearly, if
a syllable persists for a time during which the next syllable is uttered, the
two will overlap. The most important parameter to be controlled is the “
reverberation time” which is roughly the time during which the sound
persists in a hall.
If the reverberation
timeis very small the loudness is
insufficient . On the other hand, if the time of reverberation is long,there
will be confusion due to mixing of different syllables. Thus the
reverberation period should neither be too long nor small but must be of a
suitable value by which may be comfortable for both the speaker and the
audience. This suitable value of time is called optimum reverberation
time of an auditorium.
52
Reverberation Time(T) Or (RT)
Time taken for the sound to fall to the minimum audibility from the
moment when the source is cut off the production of sound is reffered as
the reverberation time(T).
Or
Reverberation time is defined as the time required by the sound energy to
reduce its intensity to 10-6 times ( one- millionth) of its original intensity
from the moment when the source of sound is cut off.
Or
The time of reverberation is also defined as the time required by the sound
energy to reduce its intensity by 60 decibels from the moment when the
source of sound is cut off.
Reverberation Time depends on the size of the hall, loudness of
sound Or the material with which the hall is made off , volume of the hall,
frequency of the sound, Intensity of sound. Reverberation time is highly
significant in the design of halls and auditoriums.
T=
A
Where V
A=
0.163 V
volume of the hall
iSi,
total amount of energy absorbed by walls and the material in the hall.
Significance of Reverberation Time
Quality of sound produced has very importance in halls, theatres, auditorium
etc. For good acoustics of a hall, the reverberation time should have an optimum
value. In a lecture hall the reverberation time should be smaller because the
speeches will clear and distinct only if a sound note decays rapidly before the next
sound note falls on the ear of listener. It is found that for a hall of 10000 cubic feet
the optimum value of reverberation time is about 1.03seconds. But for a music hall,
the reverberation time is slightly longer that there will be continuity between
successive musical notes. Hence the optimum value of reverberation time is slightly
greater than 1.03 seconds for a musical hall.
53
If the reverberation time is too small, sound vanishes very rapidly and
instantaneously. This produces a dead silence. If the reverberation time is too large,
there will be multiple reflections and successive sound notes will overlap one over
other producing confusion. Hence the listener cannot here sound distinctly. Both
too short and too long reverberation times are not good for an auditorium since they
produce unpleasantness to the listeners.
iereverberation time must be of a suitable value by which may be comfortable for
both the speaker and the audience. This suitable value of time is called optimum
reverberation time of an auditorium.
In an empty hall and in a class room with out furniture, reverberation time will
be larger. If the halls contains heavy curtains, thick carpet, card board sheets, etc.
reverberation time can be reduced considerably since these materials absorb a part
of sound energy. Open windows absorb sound energy to a large extent. Audience in
a hall is also an important factor to absorb sound energy, thereby diminishes
reverberation period. Upholstered seats are also one of the best absorber of sound.
Thus reverberation time can be suitably adjusted according to the purpose by
arranging the necessary sound absorbing materials in the auditorium. If the
audience is not full, it will be compensated with the upholstered seats since
absorbing coefficient of a person and upholstered seat is nearly 0.45 Sabine each.
Different halls with corresponding reverberation time
Different Halls
Reverberation Time
Lecture hall
0.5 to 1 sec
Conference hall and Assembly
1 to 1.5 sec
hall
Cinema theatre
1.3sec
Music recording hall
1.5 to 2 sec
Churches
1.8 to 3 sec
Sabine’s Formula
Reverberation time, 𝐓𝛂
𝐕𝐨𝐥𝐮𝐦𝐞𝐨𝐟𝐭𝐡𝐞𝐡𝐚𝐥𝐥, 𝐕
𝐕
𝐀𝐛𝐬𝐨𝐫𝐩𝐭𝐢𝐨𝐧 , 𝐀
𝐀
or 𝐓 = 𝐤
54
Where ‘K ‘is the proportionality constant. It is used to have a value of 0.161 when
the dimensions are measured in metric units.
𝑽
𝑻 = 𝟎. 𝟏𝟔𝟏 … . . (1)𝑆𝑎𝑏𝑖𝑛𝑒’𝑠𝑓𝑜𝑟𝑚𝑢𝑙𝑎
𝑨
Where A = ∑as = a1 s1 + a2 s2 + ----ansn
S1, S2...... Snare the surface areas of the absorbing materials in the hall and a1, a2 ……
an are the absorption co-efficient of the surfaces respectively. i.e., above equation
may be written as
𝑇 = 0.161
V
a1 s1  a2 s 2  .....  an s n
….. (2)
Echo
If you clap your hands from a field or valley, you can hear the same sound again
little later. This experience also due to reflection of sound. This phenomenon is
known as echo.
The first sound of clap disappeared from the ear after 1/10 second. Hence
the reflected sound of the clap from the mountain can be heard distinctly. Echo is
the same sound heard again after the original sound is heard.
Echo is the repetition of sound produced due to reflection from a distant
extended surface like a cliff, hill,buildings,etc.
Echo is produced when sound is reflected from the surface reaches the listener’s ear
after the original sound from the source has been directly heard. Echo is due to
multiple repetition of sound by the multiple reflections from the surfaces in an
enclosed hall. Sound energy prevails in a hall for 0.1 sec even after the source has
cut off the emission of sound. So one echo is distinctly heard, only if the reflected
sound reaches the listeners ears 0.1 sec after the original sound is heard directly.
Acoustics of Buildings
This is the branch of science related to architectural engineering and it deals with
the planning and construction of auditorium, cinema theatre , music hall etc. there
must be uniform intensity of sound. There must not be any focusing and
overlapping and interference of sound waves. Unwanted reflection must be avoided
and reverberation time must be minimized to its optimum value throughout.
55
Acoustic defects due to shape of room
The acoustic quality of room( hall, auditorium, studio, theatre, class room etc.)
depends on many factors such as room size, shape , extraneous noise, surface
coating, hangings and location of speaker. In this section we confine ourselves to the
acoustical phenomena related to the shape and size of the rooms. The interior shape
will determine the type of reflection and hence echoes, room flutter, dead spot and
sound foci. Room resonance id determined by the dimensions and interior coatings
of the room.
a) Echoes
Sound that reaches a listener in a room by reflections from its boundaries
takes more time than direct sound. If the time difference b/w the direct and
reflected sound is greater than 0.12s, an echo is heared. If x is the separation
b/w the listener and reflector .then,
2x
0.12 sec 
c
.12c
x
 0.06  340  20m
2
Hence a listener can hear a separate sound if the reflector is at a distance greater
than 20m. Thus, a delayed reflection produces an echo. However, it is observed that,
if the reflector is at a distance less than 20m and greater than 15m, the delayed
reflections cause a blur or mask the direct sound. Delayed reflections are most
damaging due to highly reflecting concave surfaces in the room. This defect is least if
the surface is convex, because the sound is spread out Or diffused. In whispering
galleries like GolGumbaz at Bijapur in Karnataka and St. Paul’s Cathedral in
London, multiple reflection occur due to a number of concave surfaces. A hand clap
is heard many times in GolGumbaz whispering gallery.
Concave surfaces in the room will focus sound at certain locations. As a result, some
deficiency of reflected sound occurs at some other regions of the hall or room. The
regions of deficiency of sound are called ‘dead spots’ Atdead spots sound level is
inadequate for satisfactory hearing. Care must be exercised in avoiding concave
surfaces in room.
56
b) Flutter echo
Flutter echo Or room flutter occurs between a pair of opposite walls in a
room. It is noticeable in a rectangular room with pair of opposite walls,
smooth, highly reflective, and the other pair with good absorptive materials.
An impulsive sound due to a hand clap will be heard many times due to
multiple reflections from the smooth walls. For echoes, the separation must be
greater than 20m. If the walls are nearer, reflected sound occurs frequently
and prominent flutter Or dry rattle is heard. If the separation is only 2.5m and
3m a ‘buzz’ is heard. Room flutter is occurs in uncarpeted rooms having floors
and ceiling highly reflective. Flutter echoes can be eliminated by avoiding the
use of parallel pairs of walls Or by breaking up the uniformity of such walls
with doors, windows, book shelves, paintings , hangings etc… A slit tilt of
such walls from parallel situation will efficiently reduce room flutter.
c) Sound Foci
A concave surface in the room will converge the sound into a point Or
small region called focus. Fig shows the source S and its focus S’
If S’ were the source ,S would be the focus. These two points are
interchangeable. Pair of such points are called sound foci. Many such sound
foci will be produced if many concave surfaces are present in the room. There
is an unwanted concentration of sound will be produced at S’ due to source at
S. Proper design of the surface with appropriate coating will reduce this defect.
57
d) Room Resonance
Every object has its own natural frequency of vibration. The vibration of body
due to source is called forced vibration. The vibrating air column in resonance
column apparatus is an example. It is due to the presence of excited tuning
fork. A louder sound is heard. The vibration of air column is called forced
vibration. In particular, if the natural frequency of the air column in the tube
is the same as the frequency of the fork, then air column vibrate with
maximum amplitude. It is called resonance. Due to resonance , sound
produced is maximum in intensity. This is exactly the same for air column in
a room.
The guitar string produces sound of large number of frequencies. If such
frequencies are matched with room’s natural frequencies, then resonance
occurs . As a result , sound of such frequencies resonated to give maximum
intensity. Sound of certain frequencies get amplified in the room and hence it
is a defect. This phenomenon is called room resonance.
Acoustic Requirements of a Building
Or
Common Acoustical Defects and their Remedies
In an acoustically good auditorium each syllable Or a music note produced at
a point must reach every other point in the hall clearly with equal loudness.
The following acoustical defects are common and the engineers must give
58
special attention to eliminate them during design and construction of such
buildings.
The Factors Affecting Acoustics of Buildings are
a) Reverberation
Persistence of sound energy in a hall due to multiple reflections from the walls,
ceiling etc. is called reverberation. i.e Listener hears a series of sound in addition to
the direct sound from the source. For good acoustics, the reverberation time must
have an optimum value. Reverberation time should be neither too large nor too
small. If it too large, sound notes will not be intelligible and distinct. If it is too short,
there will be a dead silence which causes unpleasantness to the listeners and
inaudibility. Using Sabine’s Formula T =
0.163 V reverberation time T can be
calculated.
A
Time of reverberation depends on size of the hall, loudness of sound and type of
speech or music for which the hall is made.
Reverberation time can be controlled by the following methods( Remedies)
1. By selecting suitable building material and furnishing materials.
2. By producing proper windows.
3. Covering walls and ceilings with sound absorbing materials like thick
curtains, perforated sheets, fibre boards, etc.
4. Covering the floor with carpets.
5. Using sound absorbing tiles.
6. Providing full audience in the auditorium. Audience absorb sound energy
considerably.
7. Furnishing with upholstered seats.
If the audience is not full, it will be compensated with upholstered chairs
because absorption of sound by a person is equivalent to absorption by an
upholstered chair.
b) Echoes
Echo is produced when the sound from a surface reaches the listener’s ear
after the original sound from the source has been directly heard. Echo is
heard if the direct sound and the reflected sound reach the listener’s ear
with a time interval of 1/7 seconds.
59
Echo is the repetition of sound waves due to multiple reflection from the
walls, ceilings etc. In an auditorium parallel and hard walls will produce
echo.
Remedy
1. Echo can be minimized by using distinct walls with sound absorbing
materials, providing thick curtains with folding etc.
2. When splayed side walls are used instead of parallel walls , echo
problem can be minimizes in an auditorium.
c) Focusing of sound Energy
If there are concave, spherical or cylindrical surfaces on walls,
ceilings and floor, sound energy will be focused to certain regions of the
auditorium. Hence there will be maximum sound at certain regions and
minimum sound at other regions. This obstructs uniform distribution of
sound in the hall and create unpleasantness.
Remedy
1. There should not be any curved surfaces on the walls, ceilings and
floors etc. If curved surfaces are present they must be covered with
suitable absorbing materials.
2. Ceiling must be low.
3. The design of the hall is so made that the speaker will be at focus of
the parabolic reelecting surface arranged behind him. This renders the
sound beam parallel and provide uniform distribution through out the
auditorium. Fan shaped floor is preffered for an acoustically fit good
auditorium for even
distribution of sound.
60
d) Adequate Loudness
There must be sufficient loudness throughout inside the hall.The large
absorption reduces loudness considerably. But loudness must not reach
below the level of hearing For sufficient loudness,
Remedy
1. Large sounding boards (polished boards) must be kept behind the
speaker.
2. Polished surfaces can be kept above the speaker.
3. Ceiling must be as low as possible.
4. Loud speakers with suitable power must be kept at proper places.
e) Resonance Effect
Hollows, cavities and air pockets etc. in the walls and ceilings will
contain air columns. These air columns select their natural frequency
from the incident sound energy and this will produce resonance. In
certain cases, windows-panes, sections of wooden potions etc. will
vibrate and produce sound waves. This may also select an equivalent
energy from the original sound and create resonance. Sometimes
61
created sound will make interference with the original sound. These
resonance and interference of sound produce distortions and hence
destroy clarity of original sound.
Remedy
1. Hollow portions, cavities and air pockets must be avoided
2. Resonant vibration must be suitably damped.
f) Echelon effect
A set of railings, regular spacing of reflecting surfaces etc. may
produce musical notes due to the regular repetition of echoes. So this
makes the original sound confusing and unintelligible. This is echelon
effect.
Remedy
Equally spaced steps, ceilings, pillars etc. must be covered with
suitable sound absorbing material.
g) Noises and Sound Insulators
Unwanted sound in an auditorium is called noise. A
noise produces displeasing effect in the listener. A noise is always a
nuisance and menace to the listener and it produces health problems,
physically and mentally. A noise may be produced by high frequency
and high intensity. Prevention of such noises is called sound
insulations Or sound proof. Noises are divided into three types (i) air
borne noises (ii) Structure borne noises and (iii) inside noise.
(i)
Air borne noise: The sound waves reaching the hall from
outside through open windows doors, ventilators, holes etc.
are called air borne noise. This is transmitted through air and
hence called air borne noise. For eg. Vehicle moving outside
produce this type of noise.
Remedy
62
1. Avoiding openings and holes.
2. Fixing doors and windows at proper places.
3. Using double doors and double windows on separate
frames with an insulating material in between them.
4. Using thick glasses or wooden boards in doors and
windows.
5. Perfectly closing doors and windows.
6. Providing double wall constructions, suspended ceiling
constructions, box type constructions etc.
(ii)
Structure borne noise
The noise propagating through the structure of the building is
called structure borne noise. This is caused by the vibration of
the structure due to different activities going on nearer to the
building. Traffic, foot steps, drilling, working of heavy
machines , working of lifts, refrigerators etc. are some
activities responsible for structure borne noise.
Remedy
1. Breaking the continuity of the building with proper sound
insulators.
2. Using anti vibration mounts.
3. Using double wall with air in between them.
4. Furnishing the floor with carpets and mats.
5. By insulating all machineries.
6. Vibrating and rotating machines must be dynamically
balanced and can be fixed on sound vibrating bed.
7. All the machines and engines must be kept in a separate
room with proper sound absorbing materials.
(iii)
Inside noise
The noise produced inside the hall is called inside noise. This
noise is produced mainly by the machines and equipments
like fans, engines, motors etc.
63
Remedy
1. Placing the machines like typewriter on absorbed pads.
2. Furnishing the floors with carpets, mats rubber sheets etc.
f) Shape and Size
Shape and size of the auditorium have important role in the
reduction of echo and reflection. A convex surface distributes sound
energy while a concave surface focuses it. In fan shaped auditorium,
there is a uniform distribution of energy.
Remedy
1. An auditorium should have sufficient and enough volume to provide
desired intensity of sound.
2. A musical hall must have a large volume where as a lecture hall
requires comparatively smaller volume. Hence the deciding factor for
the volume of a hall is its height. The ratio of height to width for an
auditorium is 2:3.
Requisites For Good Acoustics
The reverberation of sound in an auditorium is mainly due to multip;e
reflections at various surface inside. The volume and the shape of the
auditorium and the sound absorption inside influence the behavior of sound.
By varying the absorption of sound inside the hall, the reverberation time can
be brought to optimum value. The following are the essential requisites for
good acoustics:
1.
The volume of the auditorium is decided by the type of programme to be
conducted there and also number of seats to be accommodated. A musical hall
requires a large volume whereas a lecture hall requires a smaller volume . In
deciding the volume of the hall, its height plays an important rloe than its
length and breadth .The ratio of height to width for an auditorium is 2:3.
2.
The shape of the wall and ceiling should be soas to provide uniform
distribution of sound throughout the hall. The design of a hall requires smooth
decay and growth of sound. To ensure these factors the hall should have
scattering objects, walls should have irregular surface and walls must be fixed
with absorptive materials.
3.
The reverberation should be optimum. i.e, neither too large nor too small.
The reverberation time should be 0.5s to 1 sec for speech and 1 to 2 seconds
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for music. To control reverberation time, the sound absorbing materials are to
be chosen carefully.
4.
The sound heard must be sufficiently loud in every part of the hall and
no echoes should be present.
5.
The total quality of the speech and music be unchanged. i.e, the relative
intensities of the several components of a complex sound must be maintained.
6.
For a sake of clarity, the successive syllebles spoken must be clear and
distinct. i.e, there must be no confussion due to overlapping of syllables.
7.
There should be no concentration of sound in any part of the hall.
8.
The boundaries should be sufficiently sound proof to exclude extraneoys
noise.
9.
There should be no Echelon effect.
10.
There should be no resonance within the building.
11. The hall must be full Audience.
Application Of Acoustics
1.
By collecting the beam of radiation which has passed through the object
the interior structure of the object can be imaged. This method is called
acoustic tomography.
2.
SONAR refers to the application of sound in underwater. Objects in sea
can be detected and located.
3.
Acoustic Microscope is an instrument for monitoring elastic properties
in microscopic scale. It has been used o study structural details of grains and
grain boundaries of complex materials and intercellular details of biology.
4.
Echo sounderis a marine instrument used primarily for determining the
depth of water by means of an acoustic echo.
5.
Acoustic emission spectroscopy is a novel NDT technique . By
detecting acoustic waves emitted by defect
Region of a material, the defect can be evaluated.
65
Reference
8. Engineering Physics - A. Marikani
9. Engineering Physics - Randehir Singh
10.
Engineering Physics - K. Rajagopal
11.
Engineering Physics -TessyIssac
12.
Physics for Engineers -B. Premlet
13.
Engineering Physics – P.K Palanisami
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