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## Travelling Waves

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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
- Strings, water, electromagnetic
- Longitudinal
- pulses
- Displacement
- Sound

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

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

- Varies with the medium
- v = \/ B/r
- Solids and liquids
- Less compressible
- Higher Bulk modulus
- Move faster than in air

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

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 = 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

What is the intensity of a conversation at 65 dB

- = 10 log I

Io

- = log I
- 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 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)

I a1 or I1r12 = I2r22

r2

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

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

Electromagnetic (EM) Waves

- Can travel through space
- Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays
- All on the electromagnetic spectrum
- James Clerk Maxwell

- 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 = f l

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

3. Electromagnetic Spectrum

- 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

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

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

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

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

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

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