A car’s horn has a frequency of 1000 Hz. An observer hears the horn at a pitch of 1.10 kHz. If the speed of sound in air is 345
m/s, the speed that the car was travelling, relative to the
observer, is ___ m/s.

31.4 m/s

Explanation:

The Doppler equation describes how sound frequency depends on relative velocities:

fr = fs (c + vr)/(c + vs),

where fr is the frequency heard by the receiver,

fs is the frequency emitted at the source,

c is the speed of sound,

vr is the velocity of the receiver,

and vs is the velocity of the source.

Note: vr is positive if the receiver is moving towards the source, negative if away.

Conversely, vs is positive if the receiver is moving away from the source, and negative if towards.

Given:

fs = 1000 Hz

fr = 1100 Hz

c = 345 m/s

vr = 0 m/s

Find: vs

1100 = 1000 (345 + 0) / (345 + vs)

vs = -31.4

The speed of the car is 31.4 m/s.

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