Practice: The speed of sound at sea level is normally about 340 m/s. A car honks its horn as it drives toward an observer. The frequency of the horn is 800 Hz, but the observer hears an 860-Hz pitch.

What is the velocity of the car?

Show your work:

25.5 m/s

Explanation:

The Doppler effect occurs when there is relative motion between a source of a wave and an observer. In such situation, there is a shift in the apparent frequency of the wave perceived by the observer.

The formula that gives the apparent frequency perceived by the observer is:

where

f is the real frequency of the wave

f' is the apparent frequency of the wave

v is the speed of the wave

is the velocity of the source (negative if the source is moving towards the observer, positive otherwise)

is the velocity of the observer (positive if the observer is moving towards the source, negative otherwise)

In this problem:

v = 340 m/s is the speed of sound

f = 800 Hz is the frequency of the horn

f' = 860 Hz is the apparent frequency

(the observer is at rest)

Re-arranging the equation for , we can find the velocity of the horn and the driver:

So, 25.5 m/s towards the observer.

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