### Chapter 14 Waves and Energy Transfer

```Chapter 14 Waves and Energy
Transfer
Quiz 14
Chapter 14 Objectives
• Identify how waves transfer energy without
transferring matter
• Contrast transverse and longitudinal waves
• Relate wave speed, wavelength, and
frequency
Chapter 14 Objectives
• Relate a wave's speed to the medium in which
the wave travels
• Describe how waves are reflected and
refracted at boundaries between media, and
explain how waves diffract
• Apply the principle of superposition to the
phenomenon of interference
Major Ideas
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Waves and types of waves
Period and Simple harmonic motion
Crests, troughs, amplitude, wavelength
Frequency and Herz
Waves

A wiggle in space and time. Waves, like
conduction, can transfer/transmit energy from
one point to another without transporting any
matter between two points. They transfer the
energy by oscillation, by a vibration.

Disclaimer: “in space” means larger area. A bell
when struck will vibrate, but it for the most part,
stays in the same space it was before. The
sound it produces is a wave and exists over a
large area of space
Types of Waves
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Transverse waves and longitudinal waves.
Transverse waves: the motion of the
particles is perpendicular to the wave motion.
Longitudinal waves: the motion of the
particles is parallel to the wave motion.
SHM

The back and forth vibratory motion of a
wave is called simple harmonic motion (or
oscillatory motion). The simple harmonic
motion follows a sin curve over time.
Terms of Waves
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Period: How long it takes to go from crest to
crest (back to start)
Crests: The high points of a wave
(compression in longitudinal)
Troughs: The low points (rarefaction in
longitudinal)
Terms of Waves
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Midpoint: The “Home position,” the middle
of the wave
Amplitude: Distance from midpoint to crest
(or trough)
Wavelength: Length of wave, generally
measured from one crest to another
Review
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How often a vibration occurs is its frequency.
It is however many back and forth divided by
time (per second).
If two vibrations happen in a second, it then
has a 2 vibrations per second, or 2 hertz
(Hz). Hertz is the unit of frequency.


(960 AM is 960 kHz)
(so 100.7 FM is 100.7 MHz)
Random
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Some Noisy Bugs fun info
Bumblebees flap their wings with a frequency
of 130 Hz
Mosquitos about 600 Hz (or 0 Hz after you
squash it)
Questions

The Sears building in Chicago sways at
about 0.1 Hz. How many times per day does
the Sears tower sway back and forth?

How long does it take a bumble bee to flap
their wings one time? The frequency of the
wings is 130 Hz.
Question

How seconds does it take for the radio wave
98.5 FM to complete 200,000 periods/cycles?
Owning the Air
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to send out.
Introduction of DTV is so that the radio waves
can be used by other sources (police)
two messages at the same frequency.
Major Ideas
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Wave Speed and Temperature Dependence
Factors influencing wave speed (inertia and
restoring force)
v  f
Warm Up

is receiving signals with a period of 9.93E-9s.
Is the person listening to AM or FM? What is
the station?

The distance from crest to trough of a water
wave is 0.35m, what is the wavelength?
Introductory (Don’t Write)

Most information you take in today will be via wave
(sound and light (which comes to us through
electromagnetic waves)). Energy is transferred
through waves, but not matter. If you were to tie
one a rope to a wall and give it a shake (like you
would a hose), the wave moves through the medium
(the rope), but the rope stays where it was (after
being jiggled). If you drop a stone in a pond, the
ripples produce move outward, but the water stays
where it was (it goes up and comes down). When
you talk, your voice produces a wave which goes
through the room to the listener, but the air from
Wave Speed

Velocity (m/s) = wavelength (m) times
frequency (1/s)
v  f
Question

What is the wavelength of the radio station
94.1 FM? The speed of an EM wave is 3E8
m/s.
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A ripple in a pond has a frequency of 0.20
seconds and wavelength of 0.12 m. What is
the speed at which the wave travels outward?
Wave Speed Factors
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Two major things which influence the speed
of sound, the restoring force, and the
measure of inertia.
More restoring force makes wave speed
faster
More inertia makes waves slower.
What is restoring force?

It is a measure of how hard something is to
compress, with the harder to compress the
more restoring force.
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If molecules are packed tightly already (and
therefore hard to compress), the energy can be
transferred very quickly
The matter doesn’t move, but the wave does. In
order for the wave to move, it needs matter to
move through.
What is the measure of
inertia?
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It is the density. As the energy is passed
through, it is carried by the molecules.
A molecule that is very heavy, given the
same amount of energy as a molecule which
is very light, will move slower through the
propogation of the wave.
Wave Speed Comparison
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Hydrogen Gas propagates waves at a speed
of 1284 m/s. Mercury (l) propagates waves
with a speed of 1450 m/s. Since mercury is
150,000 times more dense, shouldn’t its
sound waves travel much slower? Explain.
Wave Speed dependence on
Temperature
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Temperature does have a slight effect on the
speed of sound passing through air
(molecules more energetic to begin with).
The equation is
v  v0
T
T0
Wave Speed and T
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Where T is in absolute temperature (Kelvin),
V0 is wave speed initially.
Normally you compare to 273 K (T0) which
has a V0 of 331 m/s.
Increasing Temperature does have its limits
though for increasing wave speed. Too hot
and the wave becomes incoherent.
Question
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What is the speed of a sound wave at 50 C?
Question
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You are at a concert, and the wave speed
traveling through the air is 340 m/s. Two
instruments are playing. Find the wavelength
of the note they are playing
Instrument
FrequencyWavelength
__________ 264
__________ m
__________ 396
__________ m
Major Ideas

Interference, standing waves, and
superposition
Warm Up
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A horn near the beach emits a 440 Hz sound
wave.
(a) What is the wavelength of the sound in
the air (T = 20 C)?
(b) What is the wavelength of the sound in
the water (Speed of water = 1520m/s)?
Standing Waves, Nodes, Antinodes and
Interference

While matter can not exist in the same space
and time as other matter (Two rocks can not
exist in the same place), waves can and do
(right now our bodies have bazillions of
waves passing through them). If you drop
two rocks in a pond, the waves can overlap
and form an interference pattern. The wave
effects are increased, decreased, or even
neutralized.
Types of Interference
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When a crest hits another crest, they add
together and increase amplitude. This is
called constructive interference.
When a crest hits a trough, the waves are
cancelled out, the crest “fills in” the trough.
This is called Destructive interference.
Out of Phase (180 degrees)
In Phase
Major Ideas
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Reflection, Refraction, and Diffraction
Review
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How do crests and troughs line up with
waves that are
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a) In phase?
b) Out of phase?
Explain what the Doppler effect is and how it
works.
Reflection
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Waves send energy in one direction (none
backwards) as long as there is no change in
medium (the path through which they travel).
When a wave runs into a different medium (ie
a wall) the medium changes and some of the
energy may be reflected back.
Refraction
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Not all of the energy of the wave is reflected
when coming across a boundary (change in
medium). The wave splits up: some reflects
and some transmits (passes through new
medium). The frequencies of both reflected
and transmitted wave will be the same.
However, the wave speed and wavelength
may not be
Refraction
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Frequency does not change
Velocity and Wavelength do
f 
v1
1

v2
2
Refraction
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The difference in speed causes the wave to
refract, or change the angle at which it
transmits through the material. The amount
of refraction is based off the speed difference
of the two waves
sin 1 v1

sin  2 v2
Refraction
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The angles above are angle of incidence
and angle of refraction and are measured
between the direction of the wave and the
normal.

Normal: Perpendicular to surface
Waves move faster in deep
water
Refraction
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Allows us to see pennies in the bottom of a
cup with water from the side
Keeps us from knowing exactly where the
fish is under water
Diffraction
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Diffraction is the spreading of a wave around
an obstacle in its path.
How much diffraction occurs depends on the
wavelength of the wave and the size of the
obstacle.
How much diffraction
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In general: If the wavelength is small
compared to the length/width of the obstacle,
then very little diffraction will occur. (Light
waves are very short, less than 1 micrometer
so they don’t bend around much of anything)
If the wavelength is of comparable size to the
obstacle (or larger), then bending occurs
easily. (Sound waves are about 1m in length
and bend around corners easily).
Diffraction
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When a wave passes through a gap,
diffraction is greatest when the width of the
opening is comparable to the wavelengths as
well.
Take note of how the gap produces a point
source of a wave (like dropping a pebble in a
pond)
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Following Slide
Question
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A wave in deep water is traveling at 2.4 m/s.
The wave direction is 30 degrees off of the
normal when comparing the deep water to
the shallow water.
If the wave travels at 2.0 m/s in the shallow
water, what is the angle of refraction that has
occurred?
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