Halliday, Resnick & Walker — Waves–II: Problem 64

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