Two trumpet players are both playing a pitch with a frequency of 440 Hz,corresponding to the musical pitch A above middle C.However,one of the trumpet players is marching away from you so that you hear a beat frequency of 4 Hz from the two trumpets.With what speed is the departing trumpet player moving away from you? (The speed of sound in air is 340 m/s)
A)3.12 m/s
B)3.09 m/s
C)3.06 m/s
D)3.00 m/s
E)2.95 m/s

Question

Quizplus · Accepted Answer

The beat frequency is given by the difference in frequencies heard, which is 4 Hz. Using the Doppler effect formula for a source moving away, $f' = f \left(\frac{v}{v + v_s}\right)$, where $f'$ is the observed frequency, $f$ is the source frequency (440 Hz), $v$ is the speed of sound (340 m/s), and $v_s$ is the speed of the source. The beat frequency is the difference between the source frequency and the observed frequency, so $f - f' = 4$ Hz. Solving for $v_s$ gives approximately 3.12 m/s.

Two Trumpet Players Are Both Playing a Pitch with a Frequency