Halliday, Resnick & Walker — Waves–II: Problem 104

Off-axis Doppler shift. In Fig. 17.28, a bat flies at speed \(v_b = 9.00 \text{ m/s}\) along an \(x\) axis while emitting sound at frequency \(f = 80.0 \text{ kHz}\). The sound is detected by \(D\), located at distance \(d = 20.0 \text{ m}\) off the axis. Assume that the bat is an isotropic sound source. (a) What frequency \(f'\) is detected by \(D\) when the bat emits the sound at \(x_b = -113 \text{ m}\). (Hint: What is the velocity component toward \(D\) just then?) (b) What is the bat’s coordinate at the moment of detection? (c) As the bat continues toward the origin of the coordinate system, does \(f'\) increase, decrease, or stay the same, and what is the detected frequency of the sound that is emitted at the origin?