Halliday, Resnick & Walker — Waves–II: Problem 18

In Fig. 17.10, sound waves A and B, both of wavelength \(\lambda\), are initially in phase and traveling rightward, as indicated by the two rays. Wave A is reflected from four surfaces but ends up traveling in its original direction. Wave B ends in that direction after reflecting from two surfaces. Let distance L in the figure be expressed as a multiple q of \(\lambda\): \(L = q\lambda\). What are the (a) smallest and (b) second smallest values of q that put A and B exactly out of phase with each other after the reflections?