Waves
A Basic Introduction
Vibrations and Waves
 A wave is a disturbance that carries energy
through matter (a medium) or space
 The source of all wave motion is a vibration.
 Waves transmit energy, not matter.
 Some of a wave's energy is always being
dissipated as heat. In time, this will reduce
the wave's amplitude (displacement).
 A wave cannot exist in one place but must
extend from one place to another.
 Light and sound are both examples of waves.
Waves
• A wave is a disturbance that carries energy through matter
(a medium) or space:
– Electromagnetic waves - waves that can travel through
empty space. They do not require a medium.
• EM waves are transverse waves.
• The EM spectrum consists of waves including gamma
rays, x-rays, UV light, visible light, IR waves,
microwaves and radio waves.
• EM waves travel through space at the speed of light.
– Mechanical waves – waves that must travel through some
form of matter to carry their energy. Mechanical waves
can be either transverse or longitudinal waves.
• The matter that carries a wave is called the medium and
includes matter such as air, water, rock, metal, etc.
A wave is a disturbance that carries energy through matter
(a medium) or space:
Electromagnetic
Waves
• EM waves are waves that can
travel through empty space.
They do not require a medium.
• EM waves are transverse waves.
• The EM spectrum consists of
waves including gamma rays, xrays, UV light, visible light, IR
waves, microwaves and radio
waves.
• EM waves travel through space
at the speed of light.
Mechanical Waves
• Mechanical waves are waves that
must travel through some form of
matter to carry their energy.
• The matter that carries a wave is
called the medium and includes
matter such as air, water, rock,
metal, etc.
• Mechanical waves can be either
transverse or longitudinal waves.
• In a given medium, the speed of
waves is constant. Waves travel
very quickly through solids, less
quickly through liquids and
slowest through gases.
Transverse Waves
Longitudinal Waves
• Transverse waves can be
modeled by using a sine wave.
• Longitudinal waves can be
modeled by using a spring.
• Types of transverse waves
include EM waves and ocean
waves.
• Sound waves are longitudinal
waves.
• Depending on the type of wave,
transverse waves may or may not
require a medium.
• Longitudinal waves are mechanical
waves – they require a medium.
compression
rarefaction
Waves
Waves
Electromagnetic Waves
Mechanical Waves
do not require a medium
require a medium
transverse wave
Ex: light
transverse wave
earthquake
s-waves
longitudinal wave
earthquake
p-waves
Ex: sound
Waves
Mechanical Waves
Waves carry energy, not matter. Example: waves form as wind blows across the
water's surface, transferring energy to the water. As the energy moves through
the water, so do the waves. The water itself stays behind, rising and falling in
circular movements.
•
•
•
•
The speed of a wave
depends on the medium.
In a given medium, the
speed of waves is
constant.
Kinetic theory explains
differences in wave
speed.
The closer the molecules
are, the quicker vibrations
are transferred.
Therefore, waves travel
very quickly through
solids, less quickly
through liquids and
slowest through gases.
Transverse Waves
• In transverse waves,
particles vibrate at right
angles to the direction the
wave travels.
• Transverse waves can be
modeled by using a sine
wave.
• Types of transverse waves
include EM waves and ocean
waves.
• Depending on the type of
wave, transverse waves may
or may not require a medium.
wavelength
crest
amplitude
trough
Longitudinal Waves
• In longitudinal waves,
particles vibrate back
and forth in the same
direction that the wave
travels.
• Longitudinal waves can
be modeled by using a
spring.
• Sound waves are
longitudinal waves.
• Longitudinal waves are
mechanical waves – they
require a medium.
compression
rarefaction
Wave
Pulses
Properties of Waves
• Amplitude – Maximum displacement from equilibrium. The
larger the amplitude, the more energy the wave carries.
• Wavelength – The distance between successive identical
parts of a wave. Represented by lambda, .
• Crest – The high point of a wave.
• Trough – The low point of a wave.
• Period – The time needed for a wave to make one complete
cycle (wavelength) of motion. Represented by T. Units of
seconds.
• Frequency – Number of cycles (wavelengths) per unit time.
Represented by f. Units of hertz (Hz).
Wavelength
Crest
Amplitude
Trough
Equilibrium
Position
Period and Frequency
• Period is the time needed for a wave to make one
complete cycle (wavelength) of motion. Represented by
T. Units of seconds.
• Frequency is the number of cycles (wavelengths) per unit
time. Represented by f. Units of hertz (Hz).
• Period and frequency are inverses.
– Example: Calculate the frequency of a
pendulum that has a period of 1/4 second.
– f = 1 / T = 1 / (0.25 s) = 4 Hz
Check Question
Given the equation for the speed of waves:
v=λf
Does this mean, for example, that high
frequency sounds (high pitches), travel
faster than low frequency sounds?
NO!!! Wavelength and frequency vary
inversely to produce the same speed of all
sounds. So when one goes up, the other
goes down.
Amplitude Indicates Energy
• A tsunami is
basically an
ocean wave
with a large
amplitude. It
carries
considerable
destructive
energy.
•
Photo from:
http://www.globalsecurit
y.org/military/world/thai
land/images/ik_crisp_kha
o_lak_10.jpg
Earthquakes
• Vibrations provide the energy for
waves. The bigger the vibrations,
the bigger the waves they create.
• The vibrations from earthquakes can
cause waves in the ocean and in the
ground.
• Tsunamis are giant ocean waves caused by undersea
earthquakes.
• Earthquakes cause waves in the ground called seismic
waves. Different types of seismic waves travel at
different speeds:
• P-waves are longitudinal waves; they travel the fastest.
• S-waves are transverse waves.
STOP! Check for
Understanding
• How are the frequency and period
related to each other?
• What indicates how much power a
wave has?
• What is the speed of a wave with a
frequency of 620 Hz and a
wavelength of 10.5 m?
Check for Understanding
• How are the frequency and period
related to each other?
Earthquake Waves
• Earthquakes release energy that travels through and
around the Earth in seismic waves.
• The two main types of seismic waves are body waves and
surface waves.
– Body waves can travel through Earth’s inner layers.
– Surface waves move only along the surface.
Earthquake
location
Body
wave path
Earth
Earthquake
monitoring
station
Earthquake Waves
• The two types of body waves are primary (P) waves and
secondary (S) waves.
– P waves vibrate parallel to the direction they are traveling in a
push-pull motion. P waves travel at a velocity of 4 to 6 km/s.
– S waves vibrate perpendicular to their direction of travel. S
waves travel at a velocity of 3 to 4 km/s.
• The two types of surface waves are the Love wave and
the Rayleigh wave.
– Love waves move the surface of the ground from side to side.
– Rayleigh waves roll along the surface in a circular motion, like an
ocean wave. Most of the shaking felt from an earthquake is
caused by Rayleigh waves.
– The Love wave is slightly faster than
the Rayleigh wave, but both move at
Body wave
about 4 km/s.
Earthquake
location
path
Earth
Earthquake
monitoring
station
Earthquake Check Question
A surface wave generated by an earthquake was recorded at
Seismic Station 1. Forty seconds later the same wave was
recorded at Seismic Station 2. What accounts for the time
difference?
A. The origin of the wave is closer to Seismic Station 1.
B. The speed of the wave decreases with distance.
C. The wavelength is longer at Seismic Station 2.
D. The wave frequency increases when the wave passes through soil.
Check for Understanding
• What is the speed of a wave with a
frequency of 620 Hz and a wavelength
of 10 m?
Wave Interactions
• Reflection
– Law of Reflection
– Total Internal Reflection
• Absorption
• Refraction
• Diffraction
• Interference
– Constructive
– Destructive
– Standing Waves
• Polarization
• Resonance
Wave Interactions
Anechoic Chamber
An anechoic chamber
("an-echoic" meaning
non-reflective, nonechoing or echo-free) is
a room designed to
completely absorb
reflections of either
sound or electromagnetic
waves. They are also
insulated from exterior
sources of noise.
Wave Interactions
The law of reflection
states that the angle
of incidence is equal to
the angle of reflection.
Wave Interactions
STOP! Check for
Understanding
• What is the difference between
reflection and refraction?
• Provide an example of each.
Wave Interactions
Wave Interactions – Interference
• When two or more waves are at the same place at the same time,
the resulting effect is called interference.
• Waves overlap to form an interference pattern.
• The waves combine to form a single wave.
• Constructive interference - when
the crest of one wave overlaps the
crest of another, their individual
effects add together. The result
is a wave of increased amplitude.
• Destructive interference – when
the crest of one wave overlaps the
trough of another, their individual
effects are reduced. The result is
a wave of decreased amplitude.
Check for Understanding
• What is interference?
• Is interference always a bad thing?
Polarization
• Polarization is the alignment of transverse waves.
• Polarizing light filters affect light waves the way the fence affects
the waves in the rope.
Standing Waves
• Although waves usually travel, it is possible to make a wave stay in
one place. A wave that is trapped in one spot is called a standing
wave.
• Standing waves are the result of interference. The resultant wave is
created by the interference of two waves traveling at the same
frequency, amplitude and wavelength but in opposite directions.
• In a standing wave, the nodes remain stationary.
This is where you can touch a standing wave on a
rope without disturbing the wave.
• The positions on a standing wave with the largest
amplitudes are know as antinodes. Antinodes
occur halfway between nodes.
• Standing waves can be set up on the strings of
musical instruments, in organ pipes, and by
blowing across the top of a soda bottle.
Sound Waves
 Sound waves are caused by vibrations of material objects.
 Sound waves are longitudinal waves.
 Sound waves require a medium. Sound cannot travel through a
vacuum.
 Any matter will transmit sound.
 Sound travels fastest through solids, less fast through liquids and
slowest through gasses.
 The subjective impression about the frequency of sound is pitch.
 high pitched – high frequency
 low pitched – low frequency
Frequency Ranges
The frequency range
for normal human
hearing is between 20
Hz and 20,000 Hz.
As a person ages, the
range will shrink,
especially at the high
frequency end.
Infrasonic (subsonic)
sounds have
frequencies below 20
Hz.
Ultrasonic sounds
have frequencies
above 20,000 Hz.
Sound in Air
 Compression waves travel
through air or along
springs.
 These waves travel with
areas of compressions and
rarefactions.
 Sound is a mechanical wave
– remember that it is not
the medium that travels
from one place to another,
but the pulse that travels.
Animation courtesy of Dr. Dan Russell,
Kettering University
Speed of Sound
• The speed of sound in a material depends not on the material’s density,
but on its elasticity.
• Elasticity is the ability of a material to change shape in response to an
applied force, and then resume its initial shape once the distorting
force is removed.
• Steel is elastic, putty is inelastic.
• In elastic materials, the atoms
are relatively close together and
respond quickly to each other’s
motions, transmitting energy with
little loss.
• Sound travels about fifteen times
faster in steel than in air, and
about four times faster in water
than in air.
Speed of Sound
• The speed of sound in dry air at 0C is about 330
meters per second.
• For each degree above 0C the speed of sound
increases by 0.60 meters per second.
• The speed of sound in air at normal room
temperature (~20C) is about 340 meters per
second. Use this number in calculations if no other
information is provided.
Check: How far away is a storm if you note a 3
second delay between a lightning flash and the sound
of the thunder?
340 m/sec x 3 sec = 1020 meters
Sonar
Loudness
• The intensity of a sound is proportional to
the square of the amplitude of a sound wave.
. (i = ka2)
• Sound intensity is objective and is measured
by instruments such as an oscilloscope.
• Loudness is a physiological sensation sensed
by the brain. It is subjective but related to
sound intensity.
• The unit of intensity for sound in the decibel
(dB).
• Loudness varies nearly as the logarithm of
intensity (powers of 10).
Common Levels of Sound
SOURCE OF SOUND
LEVEL (dB)
Jet Engine, at 30 m
Threshold of pain
Loud rock music
Old subway train
Average factory
Busy street traffic
Normal speech
Library
Close Whisper
Normal breathing
Hearing threshold
140
120
115
100
90
70
60
40
20
10
0
Sound Waves and
Forced Vibrations
 Resonance is a natural amplification of sound.
 All objects have their own natural frequencies at which they
are likely to vibrate.
 Vibrations can also be forced. When the frequency of a
forced vibration matches the natural frequencies of an
object, resonance occurs.
 Sounding boards are used to augment (increase) the volume
(amplitude) of a vibrating object (like a string or tuning fork).
 Sounding boards can be forced into vibrations.
 Sounding boards are important in all stringed musical
instruments.
Natural Frequency
• Everything vibrates, from planets and stars
to atoms and almost everything in between.
• A natural frequency is one at which minimum
energy is required to produce forced
vibrations.
• It is also the frequency that requires the
least amount of energy to continue this
vibration.
• Natural frequencies depend on factors such
as the elasticity and shape of the object.
Resonance
 Every object vibrates at a characteristic frequency – this
is its resonant, or natural, frequency.
 Resonance is a condition that exists when the frequency
of a force applied to a system matches the natural
frequency of the system.
 Examples of resonance are:
 Pushing a swing
 Tuning a radio station
 Voice-shattered glass.
 Tacoma Narrows Bridge Collapse in 1940.—High
winds set up standing waves in the bridge, causing the
bridge to oscillate at one of its natural frequencies.
Resonance
• When the frequency of a forced vibration on an
object matches the object’s natural frequency, a
dramatic increase in amplitude occurs. This is called
resonance.
• For example, a swing, or the hollow box parts of
musical instruments are designed to work best with
resonance.
• In order to resonate, an object must be elastic
enough to return to its original position and have
enough force applied to keep it moving (vibrating).
Sound and Resonance
 Sound travels fastest through solids, less fast through liquids and
slowest through gasses.
 Resonance is a natural amplification of sounds or vibrations.
 All objects have their own natural frequencies at which they are
likely to vibrate.
 Vibrations can also be forced. When the frequency of a forced
vibration matches the natural frequencies of an object, resonance
occurs.
 You can’t easily hear an electric guitar unless it is plugged in, but you
can easily hear a classical guitar because the body of the electric
guitar will not resonate while the hollow body of a classical guitar will
resonate.
 Resonance can be positive, such as hearing a guitar or other wood
instrument, or it can be destructive. View these videos to see the
destructive force of resonance:
 http://www.youtube.com/watch?v=17tqXgvCN0E
 http://www.youtube.com/watch?v=j-zczJXSxnw
Interference
• Sound waves interfere with each other in the
same way as all waves.
• Constructive interference - augmentation
• Destructive interference - cancellation
The Doppler Effect
• The Doppler effect is the change in observed frequency
due to the motion of the source or observer.
• The Doppler effect is the frequency shift that is the
result of relative motion between the source of waves
and an observer.
Higher frequency:
Object approaching
Lower frequency:
Object receding
• Example: As the sound of a car's horn passes and
recedes from you, the pitch of the horn seems to
decrease.
• Some application:
Echolocation (e.g., Submarines, Dolphins, Bats, etc.)
Police Radar
Weather Tracking
The Doppler Effect
http://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0076659674/78778/Doppler_Nav.swf::Doppler%20Shift%20Interactive
STATIONARY
MOVING
SOUND-GENERATING OBJECT
SOUND-GENERATING OBJECT
Velocity, v
A
Waves are created at point
source and radiate outward
creating a wave front with the
same frequency as that of the
source.
B
Although the frequency of the
sound generating object remains
constant, wave fronts reach the
observer at Point B more
frequently than Point A.
Ultrasound
• Ultrasound is cyclic high frequency sound wave
beyond the upper limit of human hearing.
• Ultrasound waves can be bounced off of tissues
using special devices. The echoes are then
converted into a picture called a sonogram.
• Ultrasound imaging (ultrasonography) allows physicians and patients to
get an inside view of soft tissues, organs, body cavities, etc., with real
time images and without using invasive techniques.
• The most well known application of ultrasound is to examine a fetus
during pregnancy.
• Ultrasound has been used to image the human body for at least 50
years. It is one of the most widely used diagnostic tools in modern
medicine.
• As currently applied in the medical environment, ultrasound poses no
known risks to the patient and there is no convincing evidence for any
danger from ultrasound during pregnancy.