Topic List

1
Topic List
W a v e s
Types of Waves Longitudinal Waves Transverse
Waves Surface Waves Frequency Wavelength Period
Amplitude
Wave speed Transmission of Waves Reflection
Refraction Superposition Principle Interference D
iffraction Standing Waves Resonance
2
Waves Information
Marvin the Martian would like to send a message
from Mars to Earth. There are two ways of
sending a message. He could enclose the message
in a rocket and physically send it to Earth. Or,
he could send some type of signal, maybe in the
form of radio waves. Information can be sent via
matter or waves. If sent via waves, nothing
material is actually transmitted from sender to
receiver. If you talk to a friend, be it in
person or on the phone, you are transmitting
information via waves. Nothing is physically
transported from you to your friend. This
would not be the case, however, if you sent him
a letter.
3
Waves Energy
Suppose Charlie Brown wants to wake up Snoopy.
Some energy is required to rouse Snoopy from his
slumber. Like information, energy can also be
transmitted via physical objects or waves.
Charlie Brown can transmit energy from himself to
Snoopy via Woodstock Woodstock flies over his
kinetic energy is physically transported in the
form a little, yellow bird. Alternatively,
Charlie Brown could send a pulse down a rope
thats attached to Snoopys dog house. The rope
itself is not transported, but the pulse and its
energy are!
pulse

4
Types of Waves
A mechanical wave is just a disturbance that
propagate through a medium. The medium could be
air, water, a spring, the Earth, or even people.
A medium is any material through which a wave
travels. Mechanical wave examples sound water
waves a pulse traveling on a spring
earthquakes a people wave in a football
stadium. An electromagnetic wave is simply light
of a visible or invisible wavelength.
Oscillating intertwined electric and magnetic
fields comprise light. Light can travel without
mediumsuper, duper fast. A matter wave is a term
used to describe particles like electrons that
display wavelike properties. It is an important
concept in quantum mechanics. A gravity wave is a
ripple in the fabric of spacetime itself. They
are predicted by Einsteins theroy of relativity,
but theyre very difficult to detect.
5
Mechanical Waves Three Types
Mechanical waves require a physical medium. The
particles in the medium can move in two different
ways either perpendicual or parallel to
direction of the wave itself. In a longitudinal
wave, the particles in the medium move parallel
to the direction of the wave. In a transverse
wave, the particles in the medium move
perpen-dicular to the direction of the wave. A
surface wave is often a combination of the two.
Particles typically move in circular or
elliptical paths at the surface of a medium.
Longitudinal ? Parallel Transverse ?
Perpendicular Surface ? Combo
6
Longitudinal Waves
A whole bunch of kids are waiting in line to get
their picture taken with Godzilla. The bully in
back pushes the kid in front of him, who bumps
into the next kid, and so on down the line. A
longitudinal pulse is sent through the line of
kids. Its longitudinal because as each kid gets
bumped, he moves forwards, then backwards (red
arrow), parallel to the direction of the pulse.
The location of the pulse is the point where two
kids are being compressed together. The next
slide shows how the pulse progresses through the
line.
pulse direction
7
Longitinal Waves (cont.)
Ouch!
C Compression (high kid density) R
Rarefaction (low kid density) The compression
(the pulse) moves up the line, but each kid keeps
his place in line.
C
Ouch!
C
R
Ouch!
I hope Godzilla eats that bully!
C
R
8
Sound is a Longitudinal Wave
As sound travels through air, water, a solid,
etc., the molecules of the medium move back and
forth in the direction of the wave, just like the
kids in the last example, except the molecules
continually move back and forth for as long as
the sound persists. If the bully kept shoving
the kid in front of
him, a series of pulses would be generated. If
he shoved with equal force each time and did this
at a regular rate, we would call these pulses a
wave. Similarly, when a speaker or a tuning fork
vibrates, it repeatedly shoves the air in front
of it, and a longitudinal wave propagates through
to the air. The speaker shoves air molecules
the bully shoves people. In either case, the
components of the medium must bump into their
neighbors.

9
Transverse Waves
After a great performance at a drum and bugle
corps contest, the audience decides to start a
wave in the stands. Each person rises and sits
at just the right time so the effect is similar
to the pulse in Charlie Browns rope. Like the
Godzilla example, people make up the wave medium
here. But this is a transverse wave because, as
the wave moves across the stands, folks are
moving up and down.
wave direction
10
Transverse Waves (cont.)
In a transverse wave, molecules arent being
compressed and spread out as they are in a
longitudinal wave. The reason a transverse wave
can propagate is because of the attraction
between adjacent molecules. Imagine if each
person in the stands on the last slide were
connected to the person on his left and right
with giant rubber bands. As soon the person on
one end stood up, the band stretches. The
tension in the band pulls his neighbor up, who,
in turn, lifts the next guy. The tension in the
rubber bands is analogous to the forces
connecting particles of the medium to their
neighbors. The colored sections of rope tug on
each other as the waves travels through them. If
they didnt, it would be as if the rope were cut,
and no wave could travel through it.

11
Surface Waves
Below the surface fluids can typically only
transmit longitudinal waves, since the attraction
between neighboring molecules is not as strong as
in a fluid. At the surface of a lake, water
molecules (white dots) move in circular paths,
which are partly longitudinal and partly
transverse. The molecules are offset, though
when one is at the top of the circle, the one in
front of it is near the top. As in any wave, the
particles of the medium do not move along with
the wave. The water molecules complete a circle
each time a crest passes by. Animation
wave direction
12
Breaking Waves
Waves break near the shore because the water
becomes shallow. Close to the shore the ground
beneath the water interferes with the circular
motions of the water molecules as they
participate in a passing wave. Sandbars further
off shore can have the same effect, much to the
delight of surfing enthusiasts like Bart.
13
Seismic Waves
Seismic waves use Earth itself as their medium.
Earthquakes produce them and so does a nation
when it carries out an underground nuclear test.
(Other countries can detect them.) Seismic waves
can be longitudinal, transverse, or surface
waves. P and S type waves are called body waves,
since they are not confined to the surface.
Rayleigh waves do most of the shaking during a
quake.
Name Type Info
P Wave Longitudinal Also known as primary, compressional, or acoustic waves fastest seismic wave
S wave Transverse Also known as secondary, or shear waves do not travel through fluids
Rayleigh Wave Surface Rolls along surface like a water wave large amplitude
Love Wave Surface Ground moves side to side as wave moves forward

14
Mini Seismic Waves
Though we might not refer to them as seismic,
anything moving on the ground can transmit waves
through the ground. If you stand near a moving
locomotive or a heard of charging elephants, you
would feel these vibrations. Even something as
small as a
beetle generates pulses when it moves. These
pulses can be detected by a nocturnal sand
scorpion. Sensors on its eight legs can detect
both longitudinal and surface waves. The
scorpion can determine the direction of the waves
based on which legs feel the waves first. It can
determine the distance of the prey based on the
time delay between the fast moving longitudinal
waves and the slower moving surface waves. The
greater the time delay, the farther away the
beetle. This is the same way seismologists
determine the distance of a quakes epicenter.
Sand is not the best conductor of waves, so the
scorpion will only be able to detect beetles
within about a half meter.
15
Wave Characteristics
Amplitude (A) Maximum displacement of particle
of the medium from its equilibrium point. The
bigger the amplitude, the more energy the wave
carries. Wavelength (?) Distance from crest
(max positive displacement) to crest same as
distance from trough (max negative displacement)
to trough. Period (T) Time it takes consecutive
crests (or troughs) to pass a given point, i.e.,
the time required for one full cycle of the wave
to pass by. Period is the reciprocal of
frequency T 1 / f. Frequency (f ) The
number of cycles passing by in a given time. The
SI unit for frequency is the Hertz (Hz), which is
one cycle per second. Wave speed (v) How fast
the wave is moving (the disturbance itself, not
how fast the individual particles are moving,
which constantly varies). Speed depends on the
medium. Well prove that v ? f.
16
Amplitude Wavelength
The red transverse wave has the same wavelength
as the longitudinal wave in the spring. (P to Q
is one full cycle.) Note that where the spring is
most compressed, the red wave is at a crest, and
where the spring is most stretched (rarified),
the red wave is at a trough. The amplitude in
the red wave is easy to see. In the longitudinal
wave, the amplitude refers to how far a particle
on the spring moves to the left or right of its
equilibrium point. Often a graph like the red
wave is used to represent a longitudinal wave.
For sound, the y-axis might be pressure deviation
from normal air pressure, and the x-axis might be
time or position.
P
Q
A
?
17
Frequency Period
Riddle me thisWhy is the frequency of a wave
the reciprocal of its period?
Answer
Period seconds per cycle. Frequency cycles
per second. Theyre reciprocals no matter what
unit we use for time. A sound wave that has a
frequency of 1,000 Hz has a period of 1 / 1,000
of a second. This means that 1,000 high pressure
fronts are moving through the air and hitting
your eardrum each second.
18
Speed, Wavelength, Frequency
Barney Rubble, a.k.a. Barney the Wave Watcher,
is excited because he just made a discovery v
? f. With some high tech, prehistoric
equipment, Barney measures the wavelength of the
incoming waves to be 18 ft. He counts 10 crests
hitting the shoreline every minute. So,
10 crests pass any given point in a time of one
minute. But 10 crests corresponds to a distance
of 180 ft, which means the wave is traveling at
180 ft / min. This result is the product of
wavelength and frequency, yielding the result
18 ft
v ? f
19
Harmonic Waves
Imagine a whole bunch of equal masses hanging
from identical springs. If the masses are set to
bobbing at staggered time intervals, a snapshot
of the masses forms a transverse wave. Each mass
undergoes simple harmonic motion, and the period
of each is the same. If the release of the
masses is timed so that the masses form a
sinusoid at each point in time, the wave is
called harmonic. Right now, m4 is peaking. A
little later m4 will be lower and m3 will be
peaking. The masses (the particles of the
medium) bob up and down but do not move
horizontally, but the wave does move horizontally.
m4
m9
m3
m8
m10
m5
m2
m7
m1
m6
wave direction
20
Making a Harmonic Wave
A generator attached to a rope moves up and down
in simple harmonic motion. This generates a
harmonic wave in the rope. Each little piece of
rope moves vertically just like the masses on the
last slide. Only the wave itself moves
horizontally. The time it takes the wave to move
from P to Q is the period of the wave, T. The
distance from P to Q is the wavelength, ?. So,
the wave speed is given by v ? / T ? f
(since frequency and period are reciprocals).
Since the generator moves vertically in SHM, the
vertical position of the black doo-jobber is
given by y(t) A cos ? t. The doo-jobbers
period is given by T 2? / ? . This is also
the period of the wave.
Q
P

wave direction
21
Making a Non-harmonic Wave
If the black doo-jobber does not move in SHM, the
wave it generates will not be harmonic. As long
as the generator has some sort of periodic
motion, the wave generated will have a well
defined period and wavelength. Here the
generator pauses at the high and low points,
causing the wave to flatten. If the wave had
moved at a constant speed and changed direction
instantly, a saw-tooth wave would have been the
result. Sound is not a transverse wave, but a
graph of pressure vs. time as a sound waves pass
by would look like a very few simple sinusoid in
the case of a pure tone. It would be a very
complicated wave if the sound is a musical
instrument of someones voice.
Q
P

wave direction
22
Wave Speed on a Rope
If a pulse is traveling along a rope to the right
at a speed v, from its point of view its still
and the rope is moving to the left at a speed v.
As the red segment of rope of length s rounds
the turn in the pulse, a centripetal force must
act on it. The tension in the rope is F, and
the downward components of the tension vectors
add to make the centripetal force.
FC m v 2 / r 2 F sin (? / 2) m v
2 / r 2 F (? / 2) m v 2 / r
(since the sine of an angle ? the
angle itself in radians) F ? m v 2 / r
F r ? / m v 2 F s
/ m v 2 (since s r ? )
m
s
(continued)
? / 2
v (rope)
? / 2
?
r
F
F

23
Wave Speed on a Rope (cont.)
If the rope is uniform density, then the mass per
unit length is a constant. Well call this
constant µ. Thus, µ m / s. From the last
slide we have
v 2 F s / m F / µ
This shows that waves travel faster in materials
that are stiff (high tension) and light weight.
Unit check N / (kg / m) ½ N m / kg
½ (kg m / s 2) m / kg ½ m 2 / s 2
½ m / s.
m
s
? / 2
? / 2
v (rope)
?
r
F
F

24
Reflection of Waves
Whenever a wave encounters different medium, some
of the wave may be reflected back, and some of
the wave penetrate and be absorbed or transmitted
through the new medium. Light waves reflects off
of objects. If it didnt, we would only be able
to see objects that emitted their own light. We
see the moon because its reflecting sunlight.
Sound waves also reflect off of objects, creating
echoes. Water waves, seismic waves, and waves
traveling on a rope all can reflect.
25
Transmission Reflection

• Lets look at 4 different scenarios of a waves
  traveling along a rope. The link below has an
  animation of each.
• Hard boundary (fixed end) Reflected wave is
  inverted.
• Soft boundary (free end) Reflected wave is
  upright.
• Light rope to heavy rope Reflected wave is
  faster and wider than transmitted wave.
  Transmitted wave is upright, but reflected wave
  is inverted (since to the thin rope, the thick
  rope is like a hard boundary).
• Heavy rope to light rope Transmitted wave is
  faster, wider, and has a greater amplitude than
  reflected wave. Both waves are upright. (The
  transmitted wave is upright this time since, to
  the thick rope, the thin rope is like a soft
  boundary).

Animation
26
Frequency of Transmitted Waves
The frequency of a transmitted wave is always
unchanged. Say a wave with a frequency of 5 Hz
is traveling along a rope that changes thickness
at some point. Since 5 pulses hit this point
every second, 5 pulses will be transmitted every
second. Since the speed will vary depending on
the thickness of the rope, the wavelength must
vary too. Here a wave travels from a thin rope to
a thick one. Because µ is larger in the thick
rope, the wave is slower there. This causes the
waves to bunch up,which means a decrease in
wavelength. (For clarity the reflected waves are
not shown here.)

v
v
27
Amplitude Energy
The energy carried by a wave is proportional to
the square of its amplitude
E ? A 2
Consider our masses on a string again. The
amount of potential energy stored in a spring is
given by U ½ k x 2, where k is the spring
constant and x is the distance from
equilibrium. For m1 or m4, U ½ k A2. The
other masses have kinetic energy but less
potential. Since energy is conserved, the total
energy any mass has
is ½ k A2. This shows that energy varies as the
square of the amplitude. The constant of
proportionality depends on the medium.

m4
m3
m5
m2
m1
28
Amplitude of Reflected Transmitted Waves
Light to Heavy
When a pulse on the light rope reaches the
interface, the heavy rope offers a lot of
resistance. The heavy rope is not affected much
by the light rope, so the transmitted pulse has a
smaller amplitude. The reflected pulses
amplitude diminishes since some of the light
ropes energy it transmitted to the heavy rope.

before

incident pulse


inverted reflected pulse


transmitted pulse
after

Back to Animation
29
Amplitude of Reflected Transmitted Waves
Heavy to Light
When a pulse on the heavy rope reaches the
interface, the light rope offers little
resistance. The light rope is greatly affected
by the heavy rope, so the transmitted pulse has a
greater amplitude. The upright reflected pulses
amplitude diminishes since some of the heavy
ropes energy it transmitted to the light rope.
incident pulse
upright reflected pulse
transmitted pulse
30
Refraction
Weve seen that when a wave reaches an interface
(a change from one medium to another), part of
the wave can be transmitted, and part can be
reflected back. A rope is a 1-dimensional
medium in a 2-dimensional medium a transmitted
wave can change direction. This is
refractionthe bending of a wave as it passes
from one medium to another. The most well know
type of refraction is that of light bending as it
passes from air to glass or water, which well
study in detail in a unit on light. As ocean
waves approach the shore at an angle, the part of
the wave closer to shore begins to slow down
because the water is shallower. This causes
refraction, and the waves bend so that it the
wave fronts (crests) come in nearly parallel with
the shore. See pic on next slide. Even though
the medium (water) doesnt change, one of its
properties doesthe speed of the wave.
31
Refraction of Ocean Waves
Wave fronts are shown in white heading toward the
beach. The water gets shallow at the bottom
first, which causes the waves to slow down and
bend, and the wavelength to decrease. By the
time the waves reach shore, theyre nearly
parallel to the shoreline. The effect can even
be seen on islands, where winds nearly wrap
around it and come toward the island from all
sides.
32
Superposition
Check out this animation to see what happens when
two pulses approach each other from opposite ends
on a rope.
Superposition Animation

• Note the following
• The waves pass through each other unaffected by
  their meeting.
• As theyre passing through each other the waves
  combine to create a changing waveform.
• The displacement of the rope at any point in this
  combo wave is the sum of the displacements of
  the displacements of the original waves. In
  other words, we add amplitudes. This is called
  superposition.

33
Constructive Destructive Interference

Destructive Interference Waves are out of
phase. By superposition, red and blue completely
cancel each other out, if their amplitudes and
frequencies are the same.
Constructive Interference Waves are in
phase. By super-position, red blue green.
If red and blue each have amplitude A, then green
has amplitude 2A.
34
Interference
Like force vectors, waves can work together or
opposition. Sometimes they can even do some of
both at the same time. Superposition applies
even when the waves are not identical.
Interference Animation
Constructive interference occurs at a point when
two waves have displacements in the same
direction. The amplitude of the combo wave is
larger either individual wave. Destructive
interference occurs at a point when two waves
have displacements in opposite directions. The
amplitude of the combo wave is smaller than that
of the wave biggest wave. Superposition can
involve both constructive and destructive
interference at the same time (but at different
points in the medium).
Wave Interference
35
Diffraction
When waves bounce off a barrier, this is
reflection. When waves bend due to a change in
the medium, this is refraction. When waves
change direction as they pass around a barrier or
through a small opening, this is diffraction.
Refraction involves a change in wave speed and
wavelength diffraction doesnt. Diffraction of
water happens as waves bend around a boat in a
harbor. This is different than the refraction of
waves near shore because the depth of water does
not decrease around the boat like it does near
shore. Diffraction is most noticeable when the
wavelength is large compared to the obstacle or
opening. Thus, no noticeable diffraction may
occur if the boat in the harbor is very big.
The sound waves from an owls hoot travel a
greater distance in the forest than a song birds
call, because a low pitch owl hoot has a longer
wavelength than a high pitch songbird call, and
the owls waves are able to diffract around
trees. Pics on next slide
36
Diffraction Pics
When waves pass a barrier they curve around it
slightly. When they pass through a small
opening, they spread out almost as if they had
come from a point source. These effects happen
for any type of wave water sound light
seismic waves, etc.
37
Diffraction Bats
Bats use ultrasonic sound waves (a frequency too
high for humans to hear) to hunt moths. The
reason they use ultrasound is because at lower
frequencies much of the sound waves would have a
wavelength close to the size of a moth, which
means much of the sound would diffract around it.
Bats hunt by echolocationbouncing sound waves
off of prey and listening for the echoes, so they
need to emit sound with a wavelength smaller that
the typical moth, which means a high frequency is
required. High frequency sound waves reflect off
the moths rather than diffracting around them.
If bats hunted bigger prey, we might have emitted
sounds that we could hear. Well learn more about
diffraction when we study light.
38
Standing Waves
Animations
When waves on a rope hits a fixed end, it
reflects and is inverted. This reflected waves
then combine with oncoming incident waves. At
certain frequencies the resulting superposition
yields a standing wave, in which some points on
the rope called nodes never move at all, and
other points called antinodes have an amplitude
twice as big as the original wave. A rope of
given length can support standing waves of many
different frequencies, called harmonics, which
are named based on the number of antinodes.
1st Harmonic ( The Fundamental )
2nd Harmonic
3rd Harmonic
4th Harmonic
continued
39
Standing Waves (cont.)
Animations
It is important to understand that a standing is
the result of the a wave interfering
constructively and destructively with its
reflection. Only certain wavelengths will
interfere with themselves and produce a standing
wave. The wavelengths that work depend on the
length of the rope, and well learn how to
calculate them in the sound unit. (Standing
waves are very important in music.) Wavelengths
that dont work result in irregular patterns. A
standing wave could be simulated with a series of
masses on springs, as long as their amplitudes
varied sinusoidally.
Standing Wave with Superposition Shown(scroll
down)
Standing Wave with Incident Reflected Waves
Shown Separately (scroll down)
40
Resonance
Objects that oscillate or vibrate tend to do so
at a particular frequency called the natural
frequency. For example, a pendulum will swing
back and forth at a certain frequency that only
depends on its length, and a mass on a spring
will bob up in down at a frequency that depends
on the mass and the spring constant. It is
possible physically to grab hold of the pendulum
or mass and force it to swing or bob at any
frequency, but if no one forces them, each will
swing of bob at its
own natural frequency. If left alone, friction
will rob the masses of their energy, and their
amplitudes will decay. If a periodic force, like
an occasional push, matches the period of one of
the masses, this is called resonance, and the
masss amplitude will grow.
M
(continued)
m
Resonance Animation
41
Resonance (cont.)
Jane does positive work
Tarzan is swinging through the jungle, but he
cant quite make it across the river to the
next tree. So, he asks Jane for a little help.
She obliges by giving him a push every time hes
just about to swing away from her. In order to
maximize his amplitude to get him across the
river, her pushing frequency must match his
natural frequency. This is resonance. When
resonance occurs her applied force does the
maximum amount of positive work. If she
mis-times the push, she might do negative work,
which would diminish his amplitude. The moral of
the story is Resonance involves timing and
matching the natural frequency of an oscillator.
When it happens, the oscillators amplitude
increases.
Jane does negative work
42
Resonance Question
Explain how you could get a 700 lb wrecking ball
swing with a large amplitude only by pulling on
it with a scrawny piece of dental floss.
answer
Give the ball a little tug, as much as you can
without breaking the floss. The ball with barely
budge. Continue giving it tugs every time the
ball is at its closest to you. If you match the
natural frequency of the ball, its amplitude will
slowly increase to the desired amount. In this
way you are adding energy to the ball very slowly.
Wrecking Ball
43
Tacoma Narrows Bridge
Even bridges have resonant (natural) frequencies.
The Tacoma Narrows bridge in Washington state
collapsed due to the complicated effects of wind.
One day in 1940 the wind blew at just the right
speed. The wind was like Jane pushing Tarzan,
and the bridge was like Tarzan. The bridge
twisted and shook
violently for about an hour. Eventually, the
vibrations caused the by wind grew in amplitude
until the bridge was destroyed.
Click the pic to see the MPEG video clip.
44
Credits
The following images were obtained for these
websites Marvin the Martian http//store.yahoo.c
om/rnrdist/warnerbrothers.html Charlie Brown
Snoopy http//www.snoopy.com/ Godzilla
http//www.cinescape.com/godzilla/ Drum Bugle
Corps (Cavaliers of Rosemont, IL)
http//www.cavaliers.org/ Sand Scorpion
http//www.aps.org/meet/MAR00/baps/vpr/layy3-03-04
.html Beach pic http//www.ssdsupply.com/hawaii.
htm Diffraction http//www.glenbrook.k12.il.us/g
bssci/phys/Class/sound/u11l3d.html
http//hea-www.harvard.edu/ECT/the_book/Chap1/Chap
ter1.html
45
Credits
Wave movies Dr. Ken Russel, Kettering
University http//www.kettering.edu/drussell/Demo
s.html Standing wave animated gifs Tom
Henderson, Glenbrook South High School
http//www.physicsclassroom.com/Class/waves/U10L4b
.html Tacoma Narrows Bridge http//www.civeng.ca
rleton.ca/Exhibits/Tacoma_Narrows/DSmith/fig06.gif