Halliday, Resnick & Walker — Waves–II: Problem 102

SHM Doppler shift. A microscopic structure is in simple harmonic motion in air along an x axis with angular frequency \(\omega = 6.80 \times 10^6 \text{ rad/s}\) (Fig. 17.26). From a stationary source, a beam of ultrasound of frequency \(f_0\) is directed toward the structure along that axis. The echo returned to a stationary detector at the ultrasound source varies in frequency during the oscillation from a lowest value \(f_L\) to a highest value \(f_H\). The ratio \(f_L/f_0\) is 0.800. (a) Where in the oscillation is the structure when \(f_L\) is emitted? What are (b) the amplitude \(x_m\) of the oscillation and (c) the ratio \(f_H/f_0\)?