Chapter 20 Traveling Waves

1. The wave model

2. One-dimensional waves

3. Sinusoidal Waves

5. Sound and Light

6. Power and Intensity

7. Doppler Effect

Stop to think 20.1 page 605Stop to think 20.2 page 607Stop to think 20.3 page 610Stop to think 20.4 page 616Stop to think 20.7 page 626

• Example 20.1 page 604• Example 20.4 page 614• Example 20.6 page 617• Example 20.9 page 621• Example 20.11 page 624

Wave Model

Traveling wave

Wave phenomena

• A bit of gossip starting in Washington reaches New York [by word of mouth] travels between these two cities. There are two quite different motions involved, that of the rumor, Washington to New York, and that of the persons who spread the rumor. The wind, passing over a field of grain, sets up a wave which spreads out across the whole field. Here again we must distinguish between the motion of the wave and the motion of the separate plants, which undergo only small oscillations… The particles constituting the medium perform only small vibrations, but the whole motion is that of a progressive wave.

• The essentially new thing here is that for the first time we consider the motion of something which is not matter, but energy propagated through matter.

Two type of wave motion

Transverse wave: vibration is perpen-dicular to the wave motion

Longitudinal wave: vibration is parallel to the direction of wave motion

One-dimensional Waves

• Basic variables of wave motion

Wavelength λ: the minimum distance between any two identical points on adjacent waves

Period T: the time required for two identical points of adjacent waves to pass by a point.

Frequency f: the inverse of the period.

Amplitude A: The maximum displacement

Wave speed V: propagating speed. V = λf

The speed of waves on strings

• If the tension in the string is T, and its mass per unit length is μ (μ =m/L)

The wave speed is :

• Ex.20.1• T = mg, μ = 0.002 kg/m

stringT

V

2string

T mgV

Sinusoidal Waves

1T

f

2

2V f

T k k

2(wave number) k

22 f

T

( , ) sin( )oD x t A kx t

Traveling in the positive x-direction

P.20.42

2( ,0) sin( )oD x A x

What is the wave speed?

P.20.41

V=4.0m/s

What is the wavelength?

Sound and Light

343 /soundV m s

Electromagnetic waves

• Electromagnetic wave speed in vacuum:• V = C = 3.00 × 108 m/s• F = V/λ• The index of Refraction:• The frequency of a wave does not change as the wave

moves from one medium to another, but λ(mat) = λ(vac)/n

speed of light in a vacuum

speed of light in the material

Cn

V

Power and Intensity

• When a wave impinges on a surface of area A ( the surface is perpendicular to the direction in which the wave is traveling), we define the intensity I : SI units W/m2

power

area

PI

A 24

sourcePI

r

The Doppler Effect

• Doppler effect: the frequency of the sound you hear is changed when the source or observer moves, this is called Doppler effect.

An observer O (the cyclist) moves with a speed Vo toward a stationary source S. The observer hears a frequency f ´ that is greater than the source frequency

'' ( )

/

o o oV V V V V V Vf f

V f V

A source S moving with a speed Vs toward a stationary observer A. Observer A hears an increased frequency

'sV

f

'' ( / ) / ( / )

V V V Vf f

Vs f V f Vs f V Vs

General case:

'V Vo

f fV Vs

How fast are the police traveling?

• A police siren has a frequency of 550 Hz as the police car approaches you, 450 Hz after it has passed you and is receding. How fast are the police traveling?

( we use the speed of sound V = 343m/s )

as police car approaches you

when car has passed you

o

s

ff

V V

o

s

ff

V V