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 = f

v = speed (m/s)

= 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/• Solids and liquids

– Less compressible– Higher Bulk modulus– Move faster than in air

Material Speed of Sound (m/s)

Air (20oC) 343

Air (0oC) 331

Water 1440

Saltwater 1560

Iron/Steel ~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 =

= 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?

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

Io (1.0 X 10-12 W/m2)

= 10 log (100) = 20 dB

Decibels: Example 2

What is the intensity of a conversation at 65 dB

= 10 log I

Io

= 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)

I 1 or I1r12 = I2r2

2

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

I = 100 W/m2

I1r12 = I2r2

2

I2 = I1r12/r2

2

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 observerf’ = f

1 - vs

v

Source moving away from stationary observerf’ = 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)

= wavelength (meters)

f = frequency (cycles/s or Hertz)

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

3. Electromagnetic Spectrum

Light

Radio Radar Micro IR Visible Light

UV X-rays

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

f = 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 = 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 = c

f= c/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