A car has front- and back-directed speakers mounted on its roof, and drives toward you with a speed of 50 ft/s, as shown in Fig.
If the speakers are driven by a 1000 Hz oscillator, what beat frequency will you hear between the direct sound and the echo off a brick building behind the car? (Take the speed of sound as 1000 ft/s.)
Text Solution
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The sound from the back-directed speaker has Doppler frequency
Where c and v are the speeds of sound and the car respectively, and v is the frequency of the sound emitted. As the wall is stationary with respect to the observer, 
is also the frequency as heard by the latter. The sound from the front-directed speaker has Doppler frequency
Hence the beat frequency is
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