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IB Physics
Waves and Sound
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The 5 Properties of Waves Rectilinear Propagation: waves
propagate (move or spread out) in straight lines in all directions away from the source.
Reflection: change in direction of a wave at an interface between two different media so that the wave returns into the medium from which it originated.
Refraction: change in direction of a wave due to a change in its speed. This is observed when a wave passes from one medium to another.
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Diffraction: bending of waves around small obstacles and the spreading out of waves passing through small openings.
Interference: the addition (superposition) of two or more waves that results in a new wave pattern.
The 5 Properties of Waves
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Any Wave: is a traveling disturbance that carries energy.
Web Link: The Wave
Two types of waves:1) Transverse – the disturbance is perpendicular to
the direction the wave is traveling
2) Longitudinal – the disturbance is parallel to the direction the wave is traveling
Web Links: Longitudinal & Transverse, Longitudinal
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?
Consider a transverse wave on a string, frozen in time:
A
A
A = Amplitude
x
y
= wavelength
Now consider the position of one point on the string:
time
y
A
A
T = period
f = frequency = 1/T
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Frequency (f), period (T), wavelength (), and wave speed (v) are all related:
If the wave crests are 12 m apart, and you see one pass by you every 3 seconds, how fast are they going?
v = /T v = f
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Ex: Radio Waves
Radio waves travel at the speed of light in a vacuum, 3.00 x 108 m/s . Find the wavelength of radio waves from “Light Rock” 106.7 FM.
How long do you think the wavelengths of radio waves are ?
Radio waves are a type of Electromagnetic Waves
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Electromagnetic WavesThese don’t need a medium (substance to travel in).
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The speed of a wave depends on the medium.
v = f That means that these two are inversely proportional
f
f
All other waves require a medium (air, water, string, etc.)
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Waves on a String
We can develop a formula for the speed of waves on a string:
v
What qualities of the string do you think determine this speed??
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Ex:
The rope has a length of 1.2 m and a mass of 2.0 kg. If he shakes the end 4.0 times a
second, and it yields the pattern shown, what is the tension in the rope?
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Sound Waves *any longitudinal waves
Sound waves in air consist of vibrating
air moleculesWeb Link: Loudspeaker
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Compare a longitudinal wave in a slinky to a sound wave in a tube:
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A = pressure amplitude = max. change in pressure
very small for common sounds ( 3x10-2 Pa)
Loudness is related to pressure amplitude
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Frequency of Sound Waves: number of cycles per second
Healthy young ears can hear frequencies between:
20 Hz 20,000 Hz
Which end do we lose with age?
UltrasonicInfrasonic
Pure tone – a single frequency sound
(most sounds are composed of many frequencies)
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Ex: Lightning & Thunder
Speed of Sound depends on the medium
(gas, liquid or solid)
vsound in air = 343 m/s (767 mi/hr)
How can you tell how far away the storm is ??
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Speed of sound in an ideal gas
vkTm
k = 1.38 x 10-23 J/K (Boltzmann const.)
T = Kelvin temperature
m = molecular mass
= CP/CV
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Ex:
Verify the speed of sound in air if the average air molecule mass is
28.9 u, and = 1.40 for air.
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Speed of sound in a liquid
vB ad
Bulk Modulus (adiabatic)
Density of liquid
Ex: Water
The speed of sound in water is around 1500 m/s
(that’s over 4 times as fast as it travels in air!)
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Speed of sound in solid bars
vY
Young’s Modulus
Ex: Train Tracks
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Sound Intensity
of the sound wave
to the wave
IPA
SI unit =
Sound Intensity = Pow erArea
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Spherically Uniform Sound:
Area = 4r2IPA
P4 r 2
How much less is the sound intensity for the person that is farther away?
600 m
200 m
Ex: Fireworks
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To compare two intensities (I and I0):
(in decibels) = 10 log (I/I0)
Notes on Sound Intensity
Intensity is related to loudness (but not directly proportional)
10-12 W/m2 = lower threshold of human hearing
1 W/m2 = enough to cause ear damage
Different sound intensities are compared using:
decibels (dB)
“Intensity Level” (unitless)
For sound meters, I0= threshold = 10-12 W/m2
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Ex:
If a sound meter picks up an intensity of 2 x 10-11 W/m2 , what
will be the intensity level reading?
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Ex:
If you bring a decibel meter to a rock concert, at what decibel reading should you start
worrying about ear damage?
(James Taylor would never play this loud……)
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Ex:
Standing 3 times as far from a uniform sound source will decrease the intensity
level by how many decibels?
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Some interesting applications of Sound Waves
Sonar:
Ex: Dolphins
Ex: Web Link: Ocean floor mapping
Ultrasound:
Web Link: How does Ultrasound work?
Cancer treatment:
Web Link: Local Hyperthermia
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The Doppler Effect-the change in wave frequency resulting from motion of the source or observer
Consider the waves from a sound source:
Now, consider the waves from a moving source:
You hear a lower frequency as it moves away
from you
You hear a higher frequency as it moves toward
you
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Web Links: Doppler Effect I and II
Doppler Effect (1 source)
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Here’s how to calculate the frequency heard by the observer:
f’ = perceived frequency
f = actual frequency
vs = speed of the source
v = speed of the wave
f f1
1v
vs
f f1
1v
vs
Source moves toward still observer
Source moves away from still observer
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Ex:
If the fire engine has a speed of 30 m/s, and its siren has a frequency of 500 Hz, what frequency does the pedestrian hear as it moves
a) toward him ?
b) away from him ?
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Now, if the observer is moving at speed vO…..
f f 1
vv
o
toward the source:
f f 1
vv
o
away from the source:
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Web Link: Doppler effect in acoustics
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Now, if both observer and source are moving…
vs
vo
(signs determined as before)
vv
1
vv
1f f
s
0