AP Physics B
(Princeton 15 &
Giancoli 11 & 12)
Waves and Sound
Preview
•  What are the two categories of waves with
regard to mode of travel?
–  Mechanical
–  Electromagnetic
•  Which type of wave requires a medium?
–  Mechanical
•  An example of a mechanical wave?
–  Sound
Velocity of a Wave
•  The speed of a wave is the distance traveled by
a given point on the wave (such as a crest) in a
given internal of time.
•  v = d/t
d: distance (m)
t: time (s)
•  v = f λ
v: speed (m/s)
λ : wavelength (m)
f : frequency (s-1, Hz)
Period of a Wave
•  T = 1/f
•  T : Period = (s)
•  F : frequency (s-1, Hz)
Problem: Sound travels at approximately
340 m/s, and light travels at 3.0 x 108 m/s.
How far away is a lightning strike if the sound
of the thunder arrives at a location 5.0
seconds after the lightning is seen?
Light travels almost instantaneously from
strike location to the observer.
The sound travels much more slowly:
d = vs t = (340 m/s)(5.0 s) = 1700m
Problem: The frequency of a C key on the
piano is 262 Hz. What is the period of this
note? What is the wavelength? Assume speed
of sound in air to be 340 m/s at 20 oC.
T = 1/f = 1/262 s-1 = 0.00382 s
V=fλ
λ = v/f
λ = 340 m/s / 262 /s = 1.30 m
Problem
•  A sound wave traveling through water has
a frequency of 500 Hz and a wavelength
of 3 m. How fast does sound travel
through water?
•  v = λ f = 3m (500 Hz) = 1500 m/s
Wave on a Wire
v=
FT
m/L
v, velocity, m/s
FT, tension on a wire, N
m/L mass/unit length, kg/m
m/L may be shown as µ
Problem Ex. 11-11
A wave whose wavelength is 0.30 m is traveling down a
300 m long wire whose total mass is 15 kg. If the tension
of the wire is 1000N, what are the speed and frequency
of the wave?
Using equation on prior slide:
v = √[( 1000N) / (15kg)(300m)]
= 140m/s
f = v / λ = 140 m/s / 0.30 m = 470 Hz
Types of Waves
•  A transverse wave is a wave in which particles
of the medium move in a direction
perpendicular to the direction which the wave
moves.
–  Example: Waves on a guitar string
•  A longitudinal wave is a wave in which particles
of the medium move in a direction parallel to the
direction which the wave moves. These are also
called compression waves.
–  Example: Sound
–  http://einstein.byu.edu/~masong/HTMstuff/
WaveTrans.html
What are two types of wave
shapes?
•  Transverse
•  Longitudinal
• 
http://www.school-for-champions.com/science/sound.htm
Transverse Wave Type
Longitudinal Wave Type
Longitudinal vs Transverse
Other Waves Types Occurring in
Nature
• 
• 
• 
• 
• 
Light: electromagnetic
Ocean waves: surface
Earthquakes: combination
Wave demos:
http://www.kettering.edu/~drussell/Demos/
waves/wavemotion.html
•  http://www.kettering.edu/~drussell/Demos/
doppler/mach1.html
Properties of Waves
•  Reflection occurs when a wave strikes a
medium boundary and “bounces back”
into the original medium.
•  Those waves completely reflected have
the same energy and speed as the original
wave.
Types of Reflection
Fixed-end ReflectionThe wave reflects with
inverted phase.
Open-end ReflectionThe wave reflects with
The same phase.
www.iop.org/activity/education/Teaching_Resources
Refraction of Waves
ü  Wave is transmitted
from one medium to
another.
ü  Refracted waves may
change speed and
Wavelength
ü  Almost always is accompanied
by some reflection.
ü  Refracted waves do not
change frequency.
Sound - a longitudinal wave
•  Sound travels through air about 340 m/s.
•  Sound travels through other media as well,
often much faster than 340 m/s.
•  Sound waves are started by vibration of
some other material, which starts the air
vibrating.
• 
www.silcom.com/~aludwig/musicand.htm
Hearing Sounds
•  We hear a sound as “high” or “low” pitch depending on
the frequency or wavelength. High-pitched sounds have
short wavelengths and high frequencies. Low-pitched
sounds have long wavelengths and low frequencies.
Humans hear from about 20 Hz to about 20,000 Hz.
•  The amplitude of a sound’s vibration is interpreted as its
loudness. We measure loudness
(also known as sound intensity)
on the decibel scale, which is
logarithmic.
http://www.allegropianoworks.com/assets/
rare_compress.jpg
Doppler Effect
•  The Doppler Effect is the apparent change in pitch of a
sound as a result of the relative motion of an observer
and the source of a sound. Coming toward you a car
horn appears higher pitched because the wavelength
has been effectively decreased by the motion of the car
relative to you. The opposite occurs when you are
behind the car.
http://people.finearts.uvic.ca/~aschloss/course_mat/MU207/images/Image2.gif
Pure Sound
•  Sounds are longitudinal waves, but they
can be shown to look like transverse
waves.
•  When air motion is graphed in a pure
sound tone versus position, we get what
looks like a sine or cosine function.
•  A tuning fork produces a relatively pure
tone as does a human whistle.
Graphing a Sound Wave
Complex Sounds
•  Because of superposition and
interference, real world waveforms may
not appear to be pure sine or cosine
functions.
•  This is because most real world sounds
are composed of multiple frequencies.
•  The human voice and most musical
instruments are examples.
The Oscilloscope
•  With an Oscilloscope we can view waveforms. Pure tones will
resemble sine or cosine functions, and complex tones will show
other repeating patterns that are formed from multiple sine and
cosine functions added together. (Amplitude vs time.)
Superposition Principle
•  When two or more waves pass a particular
point in a medium simultaneously, the
resulting displacement of the medium at
that point is the sum of the displacements
due to each individual wave.
•  The waves are said to interfere with each
other.
Superposition of Waves
•  When two or more waves meet, the
displacement at any point of the medium is
equal to the algebraic sum of the
displacements due to the individual waves.
Types of Interference
•  If the waves are in phase, when crests and
troughs are aligned, the amplitude in
increased and this is called constructive
interference.
•  If the waves are “out of phase”, when
crests and troughs are completely
misaligned, the amplitude is decreased
and can even be zero. This is called
destructive interference.
Constructive Interference
Crests are
Aligned à
the waves are
“in phase”
Destructive Interference
Crests are
aligned with
troughs à
Waves are
“out of
phase”
Constructive & Destructive
Interference
Interference Problem: Draw the waveform
from the two components shown below.