Waves and Vibrations
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Waves are everywhere in nature
Sound waves,
visible light
waves,
radio waves,
microwaves,
water waves,
sine waves,
telephone chord
waves,
stadium waves,
earthquake
waves,
waves on a
string,
slinky waves
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What is a wave?
a wave is a disturbance that travels
through a medium from one location to
another.
a wave is the motion of a disturbance
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What is a vibration?
Vibration: in a general sense, anything
that switches back and forth, to and fro,
side to side, in and out, off and on, loud
and soft, or up and down is vibrating.
Vibrations and waves: the source of all
waves is something that is vibrating.
Waves are propagations of vibrations
throughout space.
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Slinky Wave
Let’s use a slinky wave as an example.
When the slinky is stretched from end to
end and is held at rest, it assumes a
natural position known as the
equilibrium or rest position.
To introduce a wave here we must first
create a disturbance.
We must move a particle away from its
rest position.
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Slinky Wave
One way to do this is to jerk the slinky forward
the beginning of the slinky moves away from its
equilibrium position and then back.
the disturbance continues down the slinky.
this disturbance that moves down the slinky is
called a pulse.
if we keep “pulsing” the slinky back and forth,
we could get a repeating disturbance.
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Slinky Wave
This disturbance would look something like this
This type of wave is called a LONGITUDINAL wave.
The pulse is transferred through the medium of the
slinky, but the slinky itself does not actually move.
It just displaces from its rest position and then
returns to it.
So what really is being transferred?
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Slinky Wave
Energy is being transferred.
The metal of the slinky is the MEDIUM in that
transfers the energy pulse of the wave.
The medium ends up in the same place as it
started … it just gets disturbed and then returns
to it rest position.
The same can be seen with a stadium wave.
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Longitudinal Wave
The wave we see here is a longitudinal wave.
The medium particles vibrate parallel to the
motion of the pulse.
This is the same type of wave that we use to
transfer sound.
Can you figure out how??

show tuning fork demo
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Transverse waves
A second type of wave is a transverse
wave.
We said in a longitudinal wave the pulse
travels in a direction parallel to the
disturbance.
In a transverse wave the pulse travels
perpendicular to the disturbance.
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Transverse Waves
The differences between the two can be
seen
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Transverse Waves
Transverse waves occur when we wiggle
the slinky back and forth.
They also occur when the source
disturbance follows a periodic motion.
A spring or a pendulum can accomplish
this.
The wave formed here is a SINE wave.
 http://www.cleanvideosearch.com/media/action/yt/watc
h?v=X-OCz9lIiY4
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Transverse Waves
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Anatomy of a Wave
Now we can begin to describe the
anatomy of our waves.
We will use a transverse wave to describe
this since it is easier to see the pieces.
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Anatomy of a Wave
In our wave here the dashed line represents the
equilibrium position.
Once the medium is disturbed, it moves away
from this position and then returns to it
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Anatomy of a Wave
crest
The points A and F are called the CRESTS
of the wave.
This is the point where the wave exhibits the
maximum amount of positive or upwards
displacement
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Anatomy of a Wave
trough
The points D and I are called the
TROUGHS of the wave.
These are the points where the wave
exhibits its maximum negative or downward
displacement.
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Anatomy of a Wave
Amplitude
The distance between the dashed line and
point A is called the Amplitude of the wave.\
This is the maximum displacement that the
wave moves away from its equilibrium.
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Anatomy of a Wave
wavelength
The distance between two consecutive similar
points (in this case two crests) is called the
wavelength.
This is the length of the wave pulse.
Between what other points is can a wavelength be
measured?
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Anatomy of a Wave
What else can we determine?
We know that things that repeat have a
frequency and a period. How could we find
a frequency and a period of a wave?
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Wave frequency
We know that frequency measure how
often something happens over a certain
amount of time.
We can measure how many times a pulse
passes a fixed point over a given amount
of time, and this will give us the
frequency.
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Wave frequency
Suppose I wiggle a slinky back and forth,
and count that 6 waves pass a point in 2
seconds. What would the frequency be?
3 cycles / second
3 Hz
we use the term Hertz (Hz) to stand for
cycles per second.
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Wave Period
The period describes the same thing as it
did with a pendulum.
It is the time it takes for one cycle to
complete.
It also is the reciprocal of the frequency.
T = 1 / f
f = 1 / T
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Wave Speed
We can use what we know to determine
how fast a wave is moving.
What is the formula for velocity?
velocity = distance / time
What distance do we know about a wave
wavelength
and what time do we know
period
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Wave Speed
so if we plug these in we get
velocity =
length of pulse /
time for pulse to move past a fixed point
v =  / T
we will use the symbol  to represent
wavelength
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Wave Speed
v =  / T
but what does T equal
T = 1 / f
so we can also write
v = f 
velocity = frequency * wavelength
This is known as the wave equation.
examples
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14.3 Standing waves
 A wave that is
confined between
boundaries is called a
standing wave.
 With all waves,
resonance and natural
frequency are
dependent on
reflections from
boundaries of the
system containing the
wave.
14.3 Standing Waves and
Harmonics
 The standing wave with the
longest wavelength is called the
fundamental.
 The fundamental has the lowest
frequency in a series of standing
waves called harmonics.
 The first three standing wave
patterns of a vibrating string
shows that patterns occur at
multiples of the fundamental
frequency.
14.3 Energy and Waves
 All waves propagate by
exchanging energy between two
forms.
 For water and elastic strings, the
exchange is between potential and
kinetic energy.
 For sound waves, the energy
oscillates between pressure and
kinetic energy.
 In light waves, energy oscillates
between electric and magnetic
fields.
14.3 Describing Waves
 Standing waves have nodes and antinodes.
 A node is a point where the string stays at its equilibrium position.
 An antinode is a point where the wave is as far as it gets from
equilibrium.
Wave Behavior
Now we know all about waves.
How to describe them, measure them and
analyze them.
But how do they interact?
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Wave Behavior
We know that waves travel through
mediums.
But what happens when that medium runs
out?
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Boundary Behavior
The behavior of a wave when it reaches
the end of its medium is called the wave’s
BOUNDARY BEHAVIOR.
When one medium ends and another
begins, that is called a boundary.
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Fixed End
One type of boundary that a wave may
encounter is that it may be attached to a
fixed end.
In this case, the end of the medium will
not be able to move.
What is going to happen if a wave pulse
goes down this string and encounters the
fixed end?
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Fixed End
Here the incident pulse is an upward
pulse.
The reflected pulse is upside-down. It is
inverted.
The reflected pulse has the same speed,
wavelength, and amplitude as the
incident pulse.
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Fixed End Animation
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Free End
Another boundary type is when a wave’s
medium is attached to a stationary object
as a free end.
In this situation, the end of the medium is
allowed to slide up and down.
What would happen in this case?
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Free End
Here the reflected pulse is not inverted.
It is identical to the incident pulse, except
it is moving in the opposite direction.
The speed, wavelength, and amplitude
are the same as the incident pulse.
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Free End Animation
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Change in Medium
Our third boundary condition is when the
medium of a wave changes.
Think of a thin rope attached to a thin
rope. The point where the two ropes are
attached is the boundary.
At this point, a wave pulse will transfer
from one medium to another.
What will happen here?
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Change in Medium
In this situation part of the wave is reflected,
and part of the wave is transmitted.
Part of the wave energy is transferred to the
more dense medium, and part is reflected.
The transmitted pulse is upright, while the
reflected pulse is inverted.
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Change in Medium
The speed and wavelength of the reflected
wave remain the same, but the amplitude
decreases.
The speed, wavelength, and amplitude of
the transmitted pulse are all smaller than
in the incident pulse.
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Change in Medium Animation
Test your understanding
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Next let’s look at the superposition of some
simple combinations of two waves.
Superposition = overlapping of waves
The first addition of waves that will be
described involves two waves that are in
phase.
In Phase = A crest of one wave is
positioned with the crest of the other wave.
The same can be said for troughs.
This is referred to as
constructive interference.
This represents the displacement
by the white wave alone.
This represents the displacement
by the blue wave alone.
Since they are both displacements
on the same side of the baseline,
they add together.
Just repeat this step for several
points along the waves.
The next addition of waves that will be
described involves two waves that are out of
phase.
Out of phase = A crest of one wave is
positioned with a trough of the other wave.
This is referred to as
destructive interference.
This represents the displacement by the white wave alone.
This represents the displacement by the bluee wave alone.
Since the two displacements are on opposite sides of the baseline,
the top one should be considered positive and the bottom one negative.
Just add the positive and negatives together like this.
Repeat this step for several points along the waves.
Finally we observe two waves that are
partially in phase.
A different method of adding the waves will
be demonstrated.
By overlaying the constructive interference curve
from a previous slide you can tell that the curve of
this slide is not fully constructive interference.
Interference Animation
Wave Interaction
All we have left to discover is how waves
interact with each other.
When two waves meet while traveling
along the same medium it is called
INTERFERENCE.
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Constructive Interference
Let’s consider two waves moving towards
each other, both having a positive
upward amplitude.
What will happen when they meet?
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Constructive Interference
They will ADD together to produce a
greater amplitude.
This is known as CONSTRUCTIVE
INTERFERENCE.
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Destructive Interference
Now let’s consider the opposite, two
waves moving towards each other, one
having a positive (upward) and one a
negative (downward) amplitude.
What will happen when they meet?
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Destructive Interference
This time when they add together they
will produce a smaller amplitude.
This is know as DESTRUCTIVE
INTERFERENCE.
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Check Your Understanding
 Which points will produce constructive interference and
which will produce destructive interference?
 Constructive
G, J, M, N
 Destructive
H, I, K, L, O
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Waves
2 types of waves
Mechanical
Use matter to transfer energy through a medium
Electromagnetic
Do not need matter to transfer energy
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Mechanical Waves
Waves that REQUIRE a medium for the
energy to travel
Examples: water waves, sound waves,
energy moving through a slinky. What
else?
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Earthquake Waves
 Earthquakes

S wave – Transverse

P wave – Longitudinal
 Surface Waves – can travel along the
boundary
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Electromagnetic Waves
Waves that DO NOT require a medium
for the energy to travel
Examples: Light, radio waves, x-rays,
gamma rays, etc. All waves on the
electromagnetic spectrum
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Electromagnetic Waves
These waves do not need matter to travel
Difference between the different waves is
wavelength
EM spectrum illustrates the differences
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Electromagnetic Waves
Radio – listen to your
favorite station
Microwaves – call
your friends
Infrared – night
vision
Visible – you can see
this presentation
Ultraviolet – tanning
X-ray – see broken
bones
Gamma – kill
cancerous cells
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Properties of Waves
Diffraction
Interference
Reflection
Refraction
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Diffraction
Waves spread out
and bend around
corners within the
same medium.
 1) Water waves
bending around
islands
2) Water waves
passing through a slit
and spreading out
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Diffraction
Diffraction depends on the size of the
obstacle or opening compared to the
wavelength of the wave.
Less occurs if
wavelength is smaller
than the object.
More occurs if
wavelength is larger
than the object. 66
Diffraction
AM radio waves are longer and can
diffract around large buildings and
mountains; FM can’t.
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Interference
 Interference two or more
waves
overlapping to
form a new
wave.
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Constructive Interference
Constructive (in phase)
Sound waves that constructively interfere
are louder
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Destructive Interference
 Destructive (out of phase)
Sound waves that destructively interfere
are not as loud
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Interference
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Reflection
Reflection - the bouncing back of a wave.

1) Sound echoes

2) Light images in mirrors
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Refraction
Refraction - the bending of a wave
caused by a change in speed as the wave
moves from one medium to another.
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Mirage
A mirage is caused from refraction
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Sound
Sound is a mechanical wave (requires a
medium to travel) and a compressional
wave (molecules colliding)
The medium sound travels through are
molecules when they collide
Caused by the vibration of a medium
No medium; no sound.
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Sound
A tuning fork vibrates
It is vibrating, we hear the sound it
produces
But frequency is so high, we cannot
actually see the vibration.
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Sound Waves
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Sound
Often called pressure waves
Vibration produces areas of higher
pressure
These changes in pressure are recorded
by the ear drum
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Sound
We hear frequencies of sound as having
different pitch.
High frequency means more vibrations
hitting the ear.
Pitch is how high or how low a sound
seems to be.
Healthy humans can hear from 20 Hz to
20,000 Hz
We are most sensitive from 440 Hz to
7,000 Hz.
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Ultrasonic and Infrasonic
Sound
Ultrasonic sound has a frequency greater
than 20,000 Hz.
Dogs (up to 35,000 Hz)
Bats (over 100,000 Hz)
Infrasonic sound has a frequency below
20 Hz; they are felt rather than heard
earthquakes, heavy machinery
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Loudness
Loudness – sensation of intensity
Measured by the amplitude of the wave
Intensity depends on the energy in a sound
wave.
Loudness is human perception of intensity.
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Loudness
Relative to surroundings and intensity
Intensity – power per unit area
 Humans can detect intensities

as low as 10-12 W/m2
 The threshold of pain

is 1 W/m2
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Intensity of Sound
Sound intensity is usually measured in
decibels (dB)
Sound level is given as
I – intensity of the sound
I0 – threshold of hearing (10-12 W/m2)
 – sound level in dB
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Speed of Sound
The speed of sound depends on the
medium it is in, and the temperature
For air, it is calculated as
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Speed of Sound
The speed of sound has to do with the
temperature, density, and the elasticity of
the medium, so sound travels faster in
solids and liquids than it does in air.
Speeds for sound:
Air, 0 °C: 331 m/s
Air, 20 °C: 343 m/s
Water, 25 °C: 1493 m/s
Iron: 5130 m/s
Glass (Pyrex): 5640 m/s
Diamond: 12000 m/s
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Speed of Sound
Sound travels better through high-density
materials
The closer the molecules are together, the faster
they can collide and transfer energy
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Echo
An echo is when a sound wave hits a hard
surface and bounces back, causing you to
hear the sound a second time
Sonar uses echoes. It is a measure of
how long it takes the echo to return to the
source of the sound. Sonar can tell you
how far an object is from you.
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Doppler Effect
Doppler Effect – the change in pitch due
to the relative motion between a source of
sound and the receiver
Objects moving toward you have a higher
apparent frequency
Objects moving away have a lower
apparent frequency
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Doppler Effect
The general equation is
 fd= observed frequency of the detector
 fs = original frequency of the source
 v= velocity of sound in air at the T given
 vd= velocity of the detector
 vs= velocity of the source
 * The direction of the source will always be the positive
direction.
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Ex. The horn is producing a pure 1000 Hz
tone. Let’s find the frequency as heard by the
listener in various motion scenarios. The
speed of sound in air at 20 oC is 343 m/s.
A) The horn is traveling toward the source at
10 m/s and the detector is standing still
B) The horn is standing still and the detector is
moving toward the horn at 10 m/s.
C) Both the detector and the horn are moving
in the same direction. The horn is traveling at
10 m/s and the detector is traveling at 3 m/s.
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Acoustics
Acoustics is the science of sound.
 The Great Hall in the Krannert Center is an example of
excellent acoustics. Note how the walls and ceiling are
beveled to get sound waves reflect in different
directions. This minimizes the odds of there being a
“dead spot” somewhere in the audience.
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Resonance
Resonance - the ability of an object to
vibrate by absorbing energy at its natural
frequency.
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Closed Pipe Resonators
Vibrations in an closed end tube (one
end closed one open)
The closed end will always begin with a
node and the open end will produce a
louder sound when an antinode is
present at the open end.
Antinodes will also be present at every ¼
of a wavelength.
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Closed Pipe Resonators
Musical instruments such as the clarinet,
the hanging pipes under the marimbas,
and xylophones are closed pipe
resonators.
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Open Pipe Resonators
Vibrations in an open ended tube (both
ends)
At each end there is an antinode
The difference in each antinode is ½
wavelength.
Antinodes occur at every ½ wavelength
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Open Pipe Resonators
Open ended tubes produce all harmonics
– all whole number multiples of the
fundamental frequency
Musical instruments such as flutes and
saxophones are open ended resonators.
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