The Doppler Effect

Harmonic Motion and Mechanical Waves

Doppler Effect

• This effect occurs when there is motion between the source of a wave and the wave receiver. That is, the source of the wave is moving in relation to the position of the wave receiver. This is a common occurrence when dealing with sound waves.

• If the source moves away from the receiver:

In this case the frequency received will be less than the frequency given off by the source.

• If the source moves towards the receiver:

In this case the frequency received will be greater than the frequency given off by the source.

Doppler Effect

Stationary Sound Sourcesound source Shorter λ, higher

f

longer λ, lower f

www.metacafe.com/watch/961110/doppler_effect/

• The Doppler effect can be explained by the following equation:

wd s

w s

vf f

v v

fd - frequency receivedfs - source frequencyvw- speed of the wave in airvs - speed of the wave source

• When the source is moving toward you,

vw – vs

(Subtract the source speed from the speed of the wave in air)

• When the source is moving away from you, vw + vs

(Add the source speed with the speed of the wave in air)

Example: A car traveling at 20.0m/s sounds its horn which has a frequency of 240 Hz. If the speed of sound in air is

330 m/s, determine the change in frequency of the horn as the car approaches you and moves away from you.

a. CAR moves TOWARD you

330 /240

330 / 20 /

255.48387 255

wd s

w s

d

d

vf f

v v

m sf Hz

m s m s

f Hz

b. CAR moves AWAY from you

330 /240

330 / 20 /

226.2857 226

wd s

w s

d

d

vf f

v v

m sf Hz

m s m s

f Hz

1. A train blowing its whistle with a frequency of 854 Hz is moving at a speed of 140 km/h toward a stationary person. If the speed of sound is 356 m/s, what is the apparent frequency of the sound as heard by the person?

Practice

2. If the train moves away from the person in example 1 how would the apparent frequency change?

3. A car is traveling 24 m/s toward a stationary person screaming with a frequency of 345 Hz. If the speed of sound is 329 m/s, what is the apparent frequency of the sound as heard by the driver of the car?

4. How would the apparent frequency change if the car were traveling away from the person in the 1st example?

Practice:

Doppler Effect:

Textbook p. 432 #1 – 4

Air Columns: p. 298 #7 – 12, 14