Doppler Effect - GRE Subject Test: Physics

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Question

A car's horn has a frequency of $439\textup{ Hz}$ . As the car drives away from you, you hear the horn at a frequency of $384\textup{ Hz}$ . What is the speed of the car?

$v_{sound}=343\ \frac{\textup{m}}{\textup{s}}$

Answer

The equation for the Doppler effect with frequency for a moving source is given by:

$f'=\frac{f}{1\pm \frac{v_o}{v_s}}$

Where is the speed of sound, is the speed of the source, is the stationary frequency and is the Doppler frequency. Substituting the known values and solving gives us the speed of the car.

$384=\frac{439}{1\pm \frac{v_o}{343}}$

$384=439*\frac{343}{343\pm v_o}$

$384=\frac{150577}{343\pm v_o}$

$131712\pm 384v_o=150577$

$v_o=49.13\ \frac{\textup{m}}{\textup{s}}$

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