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Physics 101: Lecture 32
Waves and Sound
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Today’s lecture will cover Textbook Sections 16.1 - 16.5
Review: Simple Harmonic Motion (Chapter 10)
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Physics 101: Lecture 32, Pg 1
Review: Simple Harmonic Motion
The position x of an object moving in simple harmonic
motion as a function of time has the following form:
x = A cos (wt)
i.e. the object periodically moves back and forth between
the amplitudes x=+A and x=–A.
The time it takes for the object to make one full cycle is
the period T=2p/w=1/f, where f is the frequency of the
motion.
Thus, the angular speed in terms of T and f reads

w = 2p/T
and
w = 2 p f
Physics 101: Lecture 32, Pg 2
What is a wave ?
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Nature of waves:
A wave is a traveling disturbance that transports energy from
place to place.
There are two basic types of waves: transverse and longitudinal.
 Transverse: the disturbance travels perpendicular to the
direction of travel of the wave.
 Longitudinal: the disturbance occurs parallel to the line of
travel of the wave.
Examples:
Longitudinal: Sound waves (e.g. air moves back & forth)
Transverse: Light waves (electromagnetic waves, i.e. electric and
magnetic disturbances)
The source of the wave, i.e. the disturbance, moves continuously in
simple harmonic motion, generating an entire wave, where each
part of the wave also performs a simple harmonic motion.
Physics 101: Lecture 32, Pg 3
Types of Waves
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Transverse: The medium oscillates perpendicular to the
direction the wave is moving.
 Water waves (also have a longitudinal component)
Longitudinal: The medium oscillates in the same
direction as the wave is moving
Sound
Physics 101: Lecture 32, Pg 4
Wave Properties
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Wavelength: The distance  between identical points on the wave.
Amplitude: The maximum displacement A of a point on the wave.
Wavelength

Amplitude A
A
Physics 101: Lecture 32, Pg 5
Wave Properties...
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Period: The time T for a point on the wave to undergo one
complete oscillation.
Speed: The wave moves one wavelength  in one period T
so its speed is v = / T.
v

T
Physics 101: Lecture 32, Pg 6
v=/T
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Wave Properties...
The speed of a wave is a constant that depends only on the medium,
not on the amplitude, wavelength or period:
 and T are related !

=vT
or  = 2p v / w(since T = 2p / w
or  v / f

(since T = 1/ f )
Recall f = cycles/sec or revolutions/sec
w 2pf
Is the speed of a wave particle the same as the speed of the wave ?
No. Wave particle performs simple harmonic motion: v=A w sin wt.
Physics 101: Lecture 32, Pg 7
Concept Question
Suppose a periodic wave moves through some medium. If the period of
the wave is increased, what happens to the wavelength of the wave
assuming the speed of the wave remains the same?
correct
1. The wavelength increases
2. The wavelength remains the same
3. The wavelength decreases
Physics 101: Lecture 32, Pg 8
Concept Question
The speed of sound in air is a bit over 300 m/s, and the speed of light
in air is about 300,000,000 m/s. Suppose we make a sound wave and a
light wave that both have a wavelength of 3 meters. What is the ratio
of the frequency of the light wave to that of the sound wave?
1. About 1,000,000.
2. About 1,000.
3. About 0.000001.
correct
f = v/
fL/fS = vL/vS = 1,000,000
Physics 101: Lecture 32, Pg 9
Transverse Waves on a String (e.g. Guitar)
Speed:
T
T
v

m/L

T=Tension : the greater the tension in the string the greater
the pulling force the particles exert on each other
and the faster the wave travels.
=mass/length of the string = m/L= linear density of the spring:
the smaller the mass the greater the acceleration for
the same pulling force and the faster the wave travels.
Physics 101: Lecture 32, Pg 10
Concept Question
A rope of mass M and length L hangs from the ceiling with nothing
attached to the bottom (see picture). Suppose you start a transverse
wave at the bottom end of the rope by jiggling it a bit. As this wave
travels up the rope its speed will:
1. Increase
2. Decrease
3. Stay the same
correct
v
the tension gets greater as you go up
Physics 101: Lecture 32, Pg 11
Happy Thanksgiving !
Physics 101: Lecture 32, Pg 12