AP Physics - Wave LP
Wave 
motion of a disturbance
Waves carry Energy from one place to another
Types of Waves:
Traveling Waves
Transverse Wave - disturbance direction
perpendicular to wave direction
Longitudinal Wave - disturbance direction parallel
to wave direction
1
Transverse Wave
Longitudinal Wave
Graph of traveling wave:
Y
A
X

Amplitude, wavelength, frequency, velocity:
x
v
t
2
Wave travels  in one cycle, time is T, the period
v
But

T
1
T
f
so
v f 
35.0 cm
 Wave has frequency of Y
25.0 Hz. Find
wavelength, period,
amplitude, and
velocity of wave.
12.0 cm
X
3
Reflection; fixed end, free end
Fact: When a wave passes from one medium into another
the frequency stays the same.
4
Speed of wave on string and of sound
String
The speed is directly proportional to tension
Sound waves
The speed is directly proportional to temperature
The speed is directly proportional to density
Principle of Superposition (interference)
2 or more waves in same medium, resultant wave
equals sum of all the waves
2 traveling waves can pass through each other
.
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6
AP Physics - Sound LP
Sound  Longitudinal Wave
Audible Sound Waves  20 – 20 000 Hz
Infrasonic  frequency less than 20 Hz
Ultrasonic  frequency greater than 20 000 Hz
Speed of sound in air at 20 degree Celsius is 345 m/s
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Doppler
Perceived change in frequency due to relative motion
(velocity) between sound source and listener
Observer stationary, moving sound source:
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Shock Wave-when an object travels faster than the
speed of sound.
Atmospheric Pressure
Mach number
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Natural frequency- The frequency at which an object
tends to vibrate with when hit, struck, plucked, strummed
or somehow disturbed.
Resonance is the tendency of a system to oscillate at
maximum amplitude at a certain frequency. This
frequency is known as the system's resonance frequency
(or resonant frequency).
Tacoma narrows.
Cool thing about sound video
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Standing waves:
Incident wave and reflected wave in medium at same
time produces nodes and antinodes due to interference.
These waves can occur at more than one frequency.
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 Lowest frequency of
vibration; only one antinode (or loop)
Fundamental Frequency
First Harmonic (Fundamental frequency)
Second Harmonic
Third Harmonic
First harmonic –length of the string L=1/2 λ
Second harmonic- length of the string L = λ
Third harmonic –length of string L=3/2 λ
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Practice
A string of length L oscillates at a frequency at
which a standing wave is produced. What is the
wavelength of the wave in the string?
Practice 2
A string with a length of 3 m oscillates at a
frequency 6 Hz. What is the wavelength and
fundamental frequency?
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Standing waves in air columns (pipes)
Closed end pipes: Pipe open at one end.
First harmonic
1
4
Third harmonic
3
4
Fifth harmonic
5
4
Only odd Harmonics because at the open end there is always
an antinode.
v
fn  n
4L
n  1, 3, 5, . . .
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Open End Pipes:
First harmonic
1
2
Second harmonic
2
2
Third harmonic
3
2
All Harmonics present
Pipe Open at both ends:
fn= n v_
2L
n = 1,2,3….
Pipe Closed at one end:
v
fn  n
4L
n  1, 3, 5, . . .
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 Pipe is closed at one end, 1.50 m in length. If the speed
of sound is 345 m/s, what are the frequencies of the
first three harmonics that would be produced?
v
v
fn  n
f1 
4L
4L

m
1
f1  345 
  57.5 Hz

s  4 1.50 m  

m 
1

f3  3  345  
  172 Hz

s   4 1.50 m  

f5  f  f1   5  57.5 Hz   288 Hz
A uniform narrow tube 1.60 m long is open at both ends.
It resonates at two successive harmonics of frequencies
280 Hz and 288 Hz.
What is the fundamental frequency? What is the speed of
sound of the gas in the tube?
A pipe is 155 cm long and open at both ends. If the
speed of sound is 345 m/s. What are the frequencies of
the first three harmonics that resonate in the pipe?
16
Reflection:
Law of Reflection:
 
angle of reflection = angle of incidence (θr = θi), when
angle is measured from the normal
Normal line-line perpendicular to the boundary
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Wave direction-displacement vectors show the direction
of the wave motion.
Students draw a wave on a rope that starts with a negative
displacement and moves to the left.
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Draw standing wave- where is the speed the greatest?
Palm Pipes
12.5 Sources of Sound
- The origin of sound in musical instruments is described
- The resonant frequencies in stringed instruments is described
- Standing waves are described for a tube open at both ends and
for a tube closed at one end
12.7 Interference of Sound Waves; Beats
- The interference of sound waves and the formation of beats
are discussed
12.8 Doppler Effect
- The equations relating frequencies are derived for relative
motion between source and observer
Not in AP 1
Path Difference- difference between the paths traveled by
the sound waves. If path difference is 1/2λ then
destructive interference.
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Diffraction-spreading out of waves as it passes through
an opening. Each wave contains a wavelet (ability to
create a new wave). Hyguns principle
Reflection:
Law of Reflection:
angle of reflection = angle of incidence (θr = θi), when
angle is measured from the normal
Normal line-line perpendicular to the boundary
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 
How far away is the wall in the tuba video?
Suppose you are camping on the shore of a lake which is not
too wide, maybe 1/2 a mile across or so. During the day you
can see campers on the other side of the lake, but you cannot
hear them. At night, however, you can not only see the
campers on the other side of the lake but you can also hear
their conversations as they sit around their camp fire. This
phenomena is due to the refraction of sound waves.
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Refraction – bending of sound waves due to temperature
difference. Warmer air – sound waves travel faster.
Cooler air – sound waves travel slower.
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