A speedboat moving at 20.6 m/s sounds a signal on its horn,producing a tone of 320 Hz.There is no wind,and the speed of sound in air is 329 m/s.The apparent frequency of the sound heard by an observer in another boat moving in the opposite direction and approaching the first at a speed of 15.4 m/s is
A)282 Hz
B)287 Hz
C)316 Hz
D)357 Hz
E)369 Hz

Question

Quizplus · Accepted Answer

The apparent frequency can be calculated using the formula for the Doppler effect: $f' = f \times \frac{v + v_o}{v - v_s}$, where $f'$ is the apparent frequency, $f$ is the source frequency (320 Hz), $v$ is the speed of sound in air (329 m/s), $v_o$ is the speed of the observer relative to the medium (15.4 m/s towards the source), and $v_s$ is the speed of the source relative to the medium (20.6 m/s away from the observer). Plugging in the values, we get $f' = 320 \times \frac{329 + 15.4}{329 - 20.6} = 320 \times \frac{344.4}{308.4} \approx 357 Hz$.

A Speedboat Moving at 20