Halliday, Resnick & Walker — Waves–II: Problem 80

A detector initially moves at constant velocity directly toward a stationary sound source and then (after passing it) directly from it. The emitted frequency is \( f \). During the approach the detected frequency is \( f'_{app} \) and during the recession it is \( f'_{rec} \). If the frequencies are related by \( (f'_{app} - f'_{rec})/f = 0.500 \), what is the ratio \( v_D/v \) of the speed of the detector to the speed of sound?