Audio Engineering

90 Chapter 3

Suppose we had “ tuned ” to the peak of a 1000-Hz standing wave in a room fi rst at 72.5°F
and then later at 92.5°F. The apparent frequency shift would be

1151

113

1000 18 58

. Hz

where 1151 is the velocity (ft/s) at the temperature of measurement and 1.13 is the
wavelength at the original temperature.

3.8 Doppler Effect .........................................................................................................

We have all experienced the Doppler effect—hearing the pitch change from a higher
frequency to a lower frequency as a train whistle or a car horn comes toward a stationary
listener and then recedes into the distance. The frequency heard by the listener due to the
velocity of the source, the listener, or some combination of both is found by

F

cV

cV

L L F

S

 S

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ (3.12)

where FL is the frequency heard by the listener (observer in Hz), FS is the frequency of
the sound source in Hz,c is the velocity of sound in ft/s, VL is the velocity of the listener
in ft/s, andVS is the velocity of the sound source in ft/s.

Use minus (–) if VS in the denominator is coming toward the listener. If the listener, VL , in
the numerator is moving away from the source, use minus (–), and for the listener moving
toward the source, use plus (  ).

Example
Assume c  1130 ft/s, VL  0 , VS  60 mi/h (approaching listener), and FS  1000 Hz

60 mi

1h

1h

3600 h

5280 ft

1mi

88 ft

s



F







1130 0

1130 88

1000

1084

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

Hz.