A woman drives toward the face of a cliff at 26.8 m/s.She sounds a burst on her 500-Hz car horn and then listens for the echo.Assuming 313 m/s to be the speed of sound,the woman hears an echo frequency of
A)about 595 Hz
B)about 545 Hz
C)exactly 500 Hz
D)about 460 Hz
E)exactly 1000 Hz

Question

Quizplus · Accepted Answer

The frequency of the echo heard by the woman can be calculated using the Doppler effect formula for a moving observer and a stationary source. Since the woman is moving towards the cliff, the frequency of the sound she hears will be higher than the original frequency. The formula for the observed frequency ($f'$) when the source is stationary and the observer is moving towards the source is given by $f' = f \left(\frac{v + v_o}{v}\right)$, where $f$ is the emitted frequency (500 Hz), $v$ is the speed of sound (313 m/s), and $v_o$ is the speed of the observer (26.8 m/s). Plugging in the values, we get $f' = 500 \left(\frac{313 + 26.8}{313}\right) \approx 595$ Hz.

A Woman Drives Toward the Face of a Cliff at 26.8