Travelling Waves
Chapter 20
Waves
• Mechanical Waves
– Require a medium
– Sound, water, strings
• Electromagnetic Waves
– Can travel through a vacuum
– Radio to gamma
• Matter Waves
– Electrons and atoms
Transverse and Longitudinal
• Transverse
– Up and down
– Displacement is perpendicular to medium
– Strings, water, electromagnetic
• Longitudinal
– pulses
– Displacement
– Sound
Formula
T = 1/f
v=lf
v = speed (m/s)
l = wavelength (m)
f = frequency (cycles/s or Hz)
Example 1
A sound waves travels at 343 m/s and has a
frequency of 17,000 Hz
a. Convert the frequency to kiloHertz
b. Calculate the wavelength
Example 2
A photon has a wavelength of 5.50 X 10-7 m and a
frequency of 5.45 X 1014 Hz.
a. Calculate the speed of light
b. Calculate the period
Speed of Sound
• Varies with the medium
• v = \/ B/r
• Solids and liquids
– Less compressible
– Higher Bulk modulus
– Move faster than in air
Material
Air (20oC)
Air (0oC)
Water
Saltwater
Iron/Steel
Speed of Sound (m/s)
343
331
1440
1560
~5000
Speed of Sound: Temperature
•
•
•
•
Speed increases with temperature (oC)
v ≈ (331 + 0.60T) m/s
What is the speed of sound at 20oC?
What is the speed of sound at 2oC?
Speed of Sound: Example 1
How many seconds will it take the sound of a
lightening strike to travel 1 mile (1.6 km) if the
speed of sound is 340 m/s?
v = d/t
t = d/v
t = 1600 m/(340 m/s) ≈ 5 seconds
(count five seconds for each mile)
Pitch
• Pitch – frequency (not loudness)
• Audible range 20 Hz – 20,000 Hz
Infrasonic
Audible
Ultrasonic
20 Hz
20,000 Hz
Earthquakes
50,000 Hz (dogs)
Thunder
100,000Hz(bats)
Volcanoes
Machinery
Intensity
• Intensity = Loudness
• Louder = More pressure
• Decibel (dB) – named for Alexander Graham
Bell
• Logarithmic scale
• Intensity level =b
b = 10 log I
Io
Io = 1.0 X 10-12 W/m2
= lowest audible intensity
Example
• Rustle of leaves = 10 dB
• Whisper = 20 dB
• Whisper is 10 times as intense
Example
• Police Siren = 100 dB
• Rock Concert = 120 dB
Decibels: Example 1
How many decibels is a sound whose intensity is
1.0 X 10-10 W/m2?
b = 10 log I
Io
=
10 log (1.0 X 10-10 W/m2)
(1.0 X 10-12 W/m2)
b = 10 log (100) = 20 dB
Decibels: Example 2
What is the intensity of a conversation at 65 dB
b = 10 log I
Io
b = log I
10
Io
65 = log I
10
Io
6.5 = log I
Io
6.5 = log I – log Io
log I = 6.5 + log Io
log I = 6.5 + log (1.0 X 10-12 W/m2)
log I = 6.5 – 12 = -5.5
I = 10-5.5 = 3.16 X 10-6
Decibels: Example 3
What is the intensity of a car radio played at 106
dB?
(Ans: 1.15 X 10-11 W/m2)
Decibels: Example 4
A blender produces an intensity level of 83dB.
Calculate the decibels if a second blender is
turned on (doubles the intensity, Io = 1.0 X 10-12
W/m2).
Intensity and Distance
• Intensity = Power/area
• Inverse-squared radius
• Intensity decreases proportionally as you move
away from a sound (area of a ripple increases as
you move out)
Ia1
r2
or
I1r12 = I2r22
Distance: Example 1
The intensity level of a jet engine at 30 m is 140
dB. What is the intensity level at 300 m?
140 dB = 10 log I/Io
14 = log I/Io
14 = log I – log Io
log I = 14 + log Io = 2
I = 100 W/m2
I = 100 W/m2
I1r12 = I2r22
I2 = I1r12/r22
I2 = (100 W/m2)(30 m)2/(300 m)2
I2 = 120 dB
Distance: Example 2
If a particular English teacher talks at 80 dB when
she is 10 m away, how far would you have to
walk to reduce the sound to 40 dB? (Hint: Find
the raw intensity of each dB first).
ANS: 1000 m
Doppler Effect
•Frequency of sound changes with movement
•Moving towards you = frequency increases (higher
pitch)
•Moving away = frequency decreases (lower
frequency)
Moving Source
Source moving towards stationary observer
f’ =
f
1 - vs
v
Source moving away from stationary observer
f’ =
f
1 + vs
v
Moving Observer
Observer moving towards stationary source
f’ = 1 + vo f
v
Observer moving away from stationary source
f’ = 1 - vo f
v
Doppler Effect and the Universe
• Universe is expanding
• Evidence (Hubble’s Law)
– Only a few nearby galaxies are blueshifted
– Most are red-shifted
• Universe will probably expand forever
Doppler: Example 1
A police siren has a frequency of 1600 Hz. What
is the frequency as it moves toward you at 25.0
m/s?
f’ =
f
1 - vs
v
f’ = 1600 Hz
= 1600 Hz = 1726 Hz
[1 – (25/343)]
0.927
What will be the frequency as it moves away from
you?
f’ =
f
1 + vs
v
f’ = 1600 Hz
= 1600 Hz = 1491 Hz
[1 + (25/343)]
1.07
Doppler: Example 2
A child runs towards a stationary ice cream truck.
The child runs at 3.50 m/s and the truck’s music
is about 5000 Hz. What frequency will the child
hear?
f’ = 1 + vo f
v
f’ = 1 + vo f
v
f’ = [1+(3.50/343)]5000 Hz
f’ = (1.01)(5000 Hz) = 5051 Hz
Electromagnetic (EM) Waves
• Can travel through space
• Radio, Microwaves, IR, Light,
UV, X-rays, Gamma Rays
• All on the electromagnetic
spectrum
• James Clerk Maxwell
EM Wave
• Sinusoidal
• E and B are perpendicular to one another
• E and B are in phase
• Accelerating electric charges produce
electromagnetic waves
Wave Properties
• First man-made EM waves detected by Hertz (8
years of Maxwell’s death)
l = wavelength (meters)
f = frequency (cycles/s or Hertz)
c=fl
(in a vacuum, c = 3.00 X 108 m/s)
Light
3. Electromagnetic Spectrum
Radio Radar Micro
IR
Visible
Light
UV
Xrays
Gamma
• Visible light
• 4 X 10-7 m to 7X 10-7 m (400 to 700 nm)
• Electrons
– Radio – running electrons up and down an antenna
– Electrons moving within atoms and molecules
– X-rays - Electrons are rapidly decellerated by striking
metal
• Gamma Rays – Nuclear decay
Waves: Ex 1
Calculate the wavelength of a 60 Hz EM wave
fl=c
l = c/f
l = (3.0 X 108 m/s)/60 s-1 = 5 X 106 m
What range of the spectrum is this?
Waves: Ex 2
Calculate the wavelength of a 93.3 MHz FM radio
station
fl=c
l = c/f
l = (3.0 X 108 m/s)/(93.3 X 106 s-1) = 3.22 m
Waves: Ex 3
Calculate the frequency of 500 nm blue light.
fl=c
f = c/ l
f = (3.0 X 108 m/s)/500 X 10-9 m = 6 X 1014 Hz
Waves: Ex 4
When you speak to a telephone to someone 4000
km away, how long does it take the sound to
travel?
v = d/t
t = d/v
T = (4000 X 103 m)/(3 X 108 m/s) = 1.3 X10-2 s
Speed is less because of wires
Index of Refraction
•
•
•
•
Light slows when passing through a substance
Must be absorbed and re-emitted
Eyes slow light by ~30%
Bose-Einstein condensate (50 nanokelvins) v =
38 mph
n=c
v
v = speed in material
n = index of refraction
Refraction: Ex 1
Calculate the speed of light in water
n=c
v
v = c/n
v = (3.00 X 108 m/s)(1.33) = 2.26 X 108 m/s