11/3/2016
Waves Test
(ch. 11 and 12)
Tuesday 11/15
Wave Motion
A wave is a traveling disturbance.
A wave carries energy from place to place.
Study of a single wave pulse shows that it is begun with a vibration and
transmitted through internal forces in the medium.
Continuous waves start with vibrations too. If the vibration is SHM, then
the wave will be sinusoidal.
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Types of Waves: Transverse and Longitudinal
The motion of particles in a wave can either be
perpendicular to the wave direction (transverse)
or parallel to it (longitudinal).
Sound waves are longitudinal waves:
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Water waves are partially transverse and
partially longitudinal.
Wave Motion
Wave characteristics:
• Amplitude, A
• Wavelength, λ
• Frequency f and period T
v

T
 f
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A wave is traveling with a frequency of 200Hz.
What speed is the wave traveling at if the
wavelength is 20cm?
vf
v  (.2m)(200 Hz )
v  40m / s
AM and FM radio waves are transverse waves consisting of
electric and magnetic field disturbances traveling at a speed
of 3.00x108m/s. A station broadcasts AM radio waves whose
frequency is 1230x103Hz and an FM radio wave whose
frequency is 91.9x106Hz. Find the distance between adjacent
crests in each wave (the wavelength).
AM (v   f )
v 3.00 x108
 
 243.9m
3
f 1230 x10
FM
v 3.00 x108
 
 3.26m
6
f 91.9 x10
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The speed at which the particles on a wave
move to the right depends on how quickly
one particle of the string is accelerated
upward in response to the net pulling force.
tension
F
v
mL
length
mass
A 2.0m long string is under 20N of tension. A pulse
travels the length of the string in 50ms. What is the
mass of the string?
v
2.0m
 40m / s
0.05s
v
F
m/ L
20
m/2
40
1600 
m
40
m
 0.025kg
1600
40 
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Waves Traveling on Guitar Strings
Transverse waves travel on each string of an electric guitar after
the string is plucked. The length of each string between its two
fixed ends is 0.628 m, and the mass is 0.208 g for the highest
pitched E string and 3.32 g for the lowest pitched E string. Each
string is under a tension of 226 N. Find the speeds of the waves
on the two strings.
v
F
m L
v
226 N
0.000208kg / 0.628m
v
226
 826m / s ( HighE )
0.0003312
v
226 N
0.00332kg / 0.628m
v
226
 207 m / s ( LowE )
0.005287
Standing Waves; Resonance
Standing waves occur
when both ends of a string
are fixed. In that case, only
waves which are
motionless at the ends of
the string can persist.
There are nodes, where
the amplitude is always
zero, and antinodes, where
the amplitude varies from
zero to the maximum
value.
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The velocity of waves on a string fixed at one end
is 92 m/s. If the frequency of standing waves is
475 Hz, how far apart are two adjacent nodes?
vf

v 92m / s

 0.194m
f 475Hz
from one node to another is
1

2
1
(0.194)  0.097 m
2
Assignment
Do pg. 318-319
Problems
#36,38,41,43,44,55
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11/3/2016
Waves Test
(ch. 11 and 12)
Tuesday 11/15
1. A wave is a traveling disturbance.
2. A wave carries energy from place to place.
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Types of Waves: Transverse and Longitudinal
The motion of particles in a wave can either be
perpendicular to the wave direction (transverse) or
parallel to it (longitudinal).
Wave Speed Versus Particle Speed
Is the speed of a transverse wave on a string the same
as the speed at which a particle on the string moves?
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Reflection and Transmission of Waves
A wave reaching
the end of its
medium, but
where the
medium is still
free to move, will
be reflected (b),
and its reflection
will be upright.
A wave hitting an obstacle will be reflected (a),
and its reflection will be inverted.
Reflection and Transmission of Waves
A wave encountering a denser medium will be partly reflected and
partly transmitted; if the wave speed is less in the denser medium,
the wavelength will be shorter.
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When the pulses merge,
the Slinky assumes a
shape that is the sum of
the shapes of the
individual pulses.
The picture gives an
example of constructive
interference.
When the pulses
merge, the Slinky
assumes a shape that
is the sum of
the shapes of the
individual pulses.
The picture gives an
example of destructive
interference.
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THE PRINCIPLE OF LINEAR SUPERPOSITION
When two or more waves are present simultaneously
at the same place, the resultant disturbance is the sum
of the disturbances from the individual waves.
Refraction
If the wave enters a medium where the wave speed is
different, it will be refracted – its wave fronts and rays
will change direction.
We can calculate the angle of refraction,
which depends on both wave speeds:
(11-20)
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Refraction
The law of refraction works both ways – a wave
going from a slower medium to a faster one would
follow the red line in the other direction.
Refraction
An earthquake P wave traveling at 8.0km/s strikes
a boundary within the Earth between two kinds of
material. If it approaches the boundary at an
incident angle of 47o and the angle of refraction is
35o, what is the speed in the second medium?
sin 35o
v

sin 47 o 8.0km / s
v
0.7843 
8.0km / s
v  6.27km / s
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Diffraction
When waves encounter
an obstacle, they bend
around it, leaving a
“shadow region.” This is
called diffraction.
Diffraction
The amount of diffraction depends on the size of the obstacle
compared to the wavelength. If the obstacle is much smaller
than the wavelength, the wave is barely affected (a). If the
object is comparable to, or larger than, the wavelength,
diffraction is much more significant (b, c, d).
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Assignment
Do pg. 319-320
Problems
#63,64,66,71,72,74,76
Waves Test
(ch. 11 and 12)
Tuesday 11/15
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LONGITUDINAL SOUND WAVES
Individual air molecules are not carried along with the wave.
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Characteristics of Sound
Sound can travel through any kind of matter, but not
through a vacuum.
The speed of sound is different
in different materials; in
general, it is slowest in gases,
faster in liquids, and fastest in
solids.
The speed depends somewhat
on temperature, especially for
gases.
Characteristics of Sound
Loudness: related to intensity of the sound wave
Pitch: related to frequency.
Audible range: about 20 Hz to 20,000 Hz; upper
limit decreases with age
Ultrasound: above 20,000 Hz
Infrasound: below 20 Hz
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The frequency is the
number of cycles per
second.
A sound with a single
frequency is called a pure
tone.
The brain interprets the
frequency in terms of the
subjective quality called
pitch.
Sound waves carry energy that can be used to do work.
The amount of energy transported per second is called the
power of the wave.
The sound intensity is defined as the power that passes
perpendicularly through a surface divided by the area of that
surface.
I
P
A
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Intensity of Sound: Decibels
The intensity of a wave is the
energy transported per unit
time across a unit area.
The human ear can detect
sounds with an intensity as
low as 10-12 W/m2 and as high
as 1 W/m2.
Perceived loudness, however,
is not proportional to the
intensity.
Intensity of Sound: Decibels
The loudness of a sound is much more closely
related to the logarithm of the intensity.
Sound level is measured in decibels (dB) and is
defined:
I0 is taken to be the threshold of hearing:
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The decibel level of a jackhammer is 130 dB relative to the
threshold of hearing. Determine the decibel level if three
jackhammers operate side by side.
130dB  10 log
I
12
1.0 x10 W / m 2
13  log I  log1.0 x1012
13  log I  (12)
1  log I
I  101  10W / m 2
3 times the intensity for 3 jackhammers together
3I  30W / m 2
30W / m 2
  10 log
 135dB
1.0 x1012 W / m 2
Uniformly emitted sound
power of sound source
I
P
4 r 2
area of sphere
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11/3/2016
Two boys are whispering in the library. The radiated sound power from one
boy's mouth is 1.2 × 10–9 W; and it spreads out uniformly in all directions.
What is the minimum distance the boys must be away from the librarian so
that she will not be able to hear them? The threshold of hearing for the
librarian is 1.00 × 10–12 W/m2.
I
P
4 r 2
1.2 x10 9
1.00 x10 
12.56r 2
1.256 x10 11 r 2  1.2 x10 9
12
r 2  95.54
r  9.8m
Sources of Sound: Vibrating Strings and Air
Columns
Musical instruments produce sounds in various
ways – vibrating strings, vibrating membranes,
vibrating metal or wood shapes, vibrating air
columns.
The vibration may be started by plucking, striking,
bowing, or blowing. The vibrations are transmitted
to the air and then to our ears.
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The strings on a guitar can
be effectively shortened by
fingering, raising the
fundamental pitch.
The pitch of a string of a
given length can also be
altered by using a string of
different density.
String fixed at both ends
 v 
f n  n 
 2L 
n  1, 2, 3, 4,
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A 6.00-m long string sustains a three-loop standing wave pattern
as shown. The wave speed is 2.00 × 102 m/s.
What is the frequency of vibration?
What is the lowest possible frequency for standing waves on this
string?
Wind instruments create sound through standing
waves in a column of air.
A tube open at both ends (most wind instruments) has pressure
nodes, and therefore displacement antinodes, at the ends.
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Example
When all the holes are closed on one type of
flute, the lowest note it can sound is middle
C (261.6 Hz). If the speed of sound is 343 m/s,
and the flute is assumed to be a cylinder open
at both ends, determine the distance L.
A tube closed at one end (some organ pipes) has a
displacement node (and pressure antinode) at the closed end.
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Determine the shortest length of pipe, open at one end, which
will resonate at 256 Hz. The speed of sound is 343 m/s.
Assignment
Read
pg. 329-334
Do pg. 347
Problems
#2,5,8,11,16,21,
25,27,30,33,35
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11/3/2016
Waves Test
(ch. 11 and 12)
Tuesday 11/15
THE PRINCIPLE OF LINEAR SUPERPOSITION
When two or more waves are present simultaneously at the same
place, the resultant disturbance is the sum of the disturbances
from the individual waves.
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11/3/2016
When two waves always meet condensation-tocondensation and rarefaction-to-rarefaction, they are
said to be exactly in phase and to exhibit constructive
interference.
When two waves always meet condensation-torarefaction, they are said to be exactly out of phase
and to exhibit destructive interference.
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When two waves always meet condensation-torarefaction, they are said to be exactly out of phase
and to exhibit destructive interference.
If the wave patters do not shift relative to one another as time
passes, the sources are said to be coherent.
For two wave sources vibrating in phase, a difference in path lengths that
is zero or an integer number (1, 2, 3, . . ) of wavelengths leads to constructive
interference; a difference in path lengths that is a half-integer number
(½ , 1 ½, 2 ½, . .) of wavelengths leads to destructive interference.
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Forced Vibrations; Resonance
• Forced vibrations occur when there is a periodic
driving force. This force may or may not have the
same period as the natural frequency of the system.
• If the frequency is the same as the natural frequency,
the amplitude becomes quite large. This is called
resonance.
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Forced Vibrations; Resonance
Interference of Sound Waves; Beats
Waves can also interfere in time, causing a phenomenon
called beats. Beats are the slow “envelope” around two waves
that are relatively close in frequency.
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Interference of Sound Waves; Beats
Doppler Effect
The Doppler effect occurs when a source of sound is
moving with respect to an observer.
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Doppler Effect
As can be seen in the previous image, a source
moving toward an observer has a higher
frequency and shorter wavelength; the opposite is
true when a source is moving away from an
observer.
Doppler Effect
If the observer is moving with respect to the source, things are a bit different.
The wavelength remains the same, but the wave speed is different for the
observer.
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If the source is moving away from the stationary observer:
f
f '
 vsource 
1 

 vsound 
If the source is moving towards the observer:
f
f '
 vsource 
1 

 vsound 
We find, for an observer moving towards a stationary source:
 v

f '  1  source  f
 vsound 
And if it is moving away:
 v

f '  1  source  f
 vsound 
The Sound of a Passing Train
A high-speed train is traveling at a speed of 44.7 m/s when the
engineer sounds the 415-Hz warning horn. The speed of sound is
343 m/s. What are the frequency and wavelength of the sound,
as perceived by a person standing at the crossing, when the train
is (a) approaching and (b) leaving the crossing?
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By scanning ultrasonic waves across the body and
detecting the echoes from various locations, it is
possible to obtain an image.
Ultrasonic sound waves cause
the tip of the probe to vibrate at
23 kHz and shatter sections of
the tumor that it touches.
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When the sound is reflected
from the red blood cells, its
frequency is changed in a
kind of Doppler effect because
the cells are moving.
Assignment
Do pg. 348
Problems
#41,43,46,50,52
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