Halliday, Resnick & Walker — Waves-II: Problem 51

51 Two loud speakers are located 3.35 m apart on an outdoor stage. A listener is 17.5 m from one and 19.5 m from the other. During the sound check, a signal generator drives the two speakers in phase with the same amplitude and frequency. The transmitted frequency is swept through the audible range (20 Hz to 20 kHz). (a) What is the lowest frequency \(f_{\min,1}\) that gives minimum signal (destructive interference) at the listener’s location? By what number must \(f_{\min,1}\) be multiplied to get (b) the second lowest frequency \(f_{\min,2}\) that gives minimum signal and (c) the third lowest frequency \(f_{\min,3}\) that gives minimum signal? (d) What is the lowest frequency \(f_{\max,1}\) that gives maximum signal (constructive interference) at the listener’s location? By what number must \(f_{\max,1}\) be multiplied to get (e) the second lowest frequency \(f_{\max,2}\) that gives maximum signal and (f) the third lowest frequency \(f_{\max,3}\) that gives maximum signal?