CK-12-Physics - Intermediate

http://www.ck12.org Chapter 11. Vibrations and Sound

FIGURE 11.25

v=λf → λ=

v

f

Double the frequency means half the wavelength, and vice versa. The pitch sounds high as the car approaches, and
low after it goes past.

Using this, we can figure out exactly what the change is. When the car is going away, the wavelength is longer by
exactly how far the car moves during the time of one period,T=^1 f. As before, we will call the wave speedvThe
car is the source of the wave, so its velocity is labeledvsfor velocity of the source. Then the effectively longer
wavelengthλ′(called “lambda prime”) is:

λ′=λ+vT=

(

v

f

)

+

(

vs

f

)

=

v+vs

f

This can alternately be expressed by what the effective new frequencyf′is compared to the original frequencyf.

f′=

v

λ′

=v

(

f

v+vs

)

=f

v

v+vs

The denominator here is larger, so this longer wavelength means a smaller frequency. It will be heard as a lower
pitch or note.

If the car is approaching us, then the new wavelength is shorter by the same amount. We can use the same equation,
but put in a negative value for the velocity of the sourcevs.

• Positivevs is the source moving away for longer wavelength.


• Negativevs is the source moving closer for shorter wavelength.

Moving Observer, Stationary Source

A similar effect is true if you are in a car going past a source of sound. There is a small but important difference,
though, because we assume that the air is stationary and the sound moves at a fixed speed through the air. Therefore,