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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

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Travelling Waves


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waves
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 and Longitudinal
  • Transverse
    • Up and down
    • Displacement is perpendicular to medium
    • Strings, water, electromagnetic
  • Longitudinal
    • pulses
    • Displacement
    • Sound
formula
Formula

T = 1/f

v = l f

v = speed (m/s)

l = wavelength (m)

f = frequency (cycles/s or Hz)

example 1
Example 1

A sound waves travels at 343 m/s and has a frequency of 17,000 Hz

  • Convert the frequency to kiloHertz
  • Calculate the wavelength
example 2
Example 2

A photon has a wavelength of 5.50 X 10-7 m and a frequency of 5.45 X 1014 Hz.

  • Calculate the speed of light
  • Calculate the period
speed of sound
Speed of Sound
  • Varies with the medium
  • v = \/ B/r
  • Solids and liquids
    • Less compressible
    • Higher Bulk modulus
    • Move faster than in air
slide8
Material Speed of Sound (m/s)

Air (20oC) 343

Air (0oC) 331

Water 1440

Saltwater 1560

Iron/Steel ~5000

speed of sound temperature
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
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
  • 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
  • Intensity = Loudness
  • Louder = More pressure
  • Decibel (dB) – named for Alexander Graham Bell
  • Logarithmic scale
  • Intensity level =b
slide13
b = 10 log I

Io

Io = 1.0 X 10-12 W/m2

= lowest audible intensity

slide14
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
Decibels: Example 1

How many decibels is a sound whose intensity is 1.0 X 10-10 W/m2?

b = 10 log I = 10 log (1.0 X 10-10 W/m2)

Io (1.0 X 10-12 W/m2)

b = 10 log (100) = 20 dB

decibels example 2
Decibels: Example 2

What is the intensity of a conversation at 65 dB

  • = 10 log I

Io

  • = log I
  • Io

65 = log I

10 Io

slide17
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
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
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 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)

I a1 or I1r12 = I2r22

r2

distance example 1
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

slide22
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
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
Doppler Effect
  • Frequency of sound changes with movement
  • Moving towards you = frequency increases (higher pitch)
  • Moving away = frequency decreases (lower frequency)
moving source
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
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
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
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

slide29
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
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

slide31
f’ = 1 + vo f

v

f’ = [1+(3.50/343)]5000 Hz

f’ = (1.01)(5000 Hz) = 5051 Hz

electromagnetic em waves
Electromagnetic (EM) Waves
  • Can travel through space
  • Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays
  • All on the electromagnetic spectrum
  • James Clerk Maxwell
slide33

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
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 = f l

(in a vacuum, c = 3.00 X 108 m/s)

slide35

Light

3. Electromagnetic Spectrum

slide36

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
Waves: Ex 1

Calculate the wavelength of a 60 Hz EM wave

f l = c

  • = c/f
  • = (3.0 X 108 m/s)/60 s-1 = 5 X 106 m

What range of the spectrum is this?

waves ex 2
Waves: Ex 2

Calculate the wavelength of a 93.3 MHz FM radio station

f l = c

  • = c/f
  • = (3.0 X 108 m/s)/(93.3 X 106 s-1) = 3.22 m
waves ex 3
Waves: Ex 3

Calculate the frequency of 500 nm blue light.

f l = c

f= c/ l

f = (3.0 X 108 m/s)/500 X 10-9 m = 6 X 1014 Hz

waves ex 4
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
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
slide42

n = c

v

v = speed in material

n = index of refraction

refraction ex 1
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