Halliday, Resnick & Walker — Waves-II: Problem 57

57 In Fig. 17-34, two speakers separated by distance $d_1 = 2.00 \text{ m}$ are in phase. Assume the amplitudes of the sound waves from the speakers are approximately the same at the listener’s ear at distance $d_2 = 4.00 \text{ m}$ directly in front of one speaker. Consider the full audible range for normal hearing, $20 \text{ Hz}$ to $20 \text{ kHz}$. (a) What is the lowest frequency $f_{\text{min},1}$ that gives minimum signal (destructive interference) at the listener’s ear? By what number must $f_{\text{min},1}$ be multiplied to get (b) the second lowest frequency $f_{\text{min},2}$ that gives minimum signal and (c) the third lowest frequency $f_{\text{min},3}$ that gives minimum signal? (d) What is the lowest frequency $f_{\text{max},1}$ that gives maximum signal (constructive interference) at the listener’s ear? By what number must $f_{\text{max},1}$ be multiplied to get (e) the second lowest frequency $f_{\text{max},2}$ that gives maximum signal and (f) the third lowest frequency $f_{\text{max},3}$ that gives maximum signal?