Two loudspeakers, separated by a distance of d1 = 2.20 m , are in phase. Assume

Question

Two loudspeakers, separated by a distance of d1 = 2.20 m, are in phase. Assume the amplitudes of the sound from the speakers are approximately the same at the position of a listener, who is d2 = 4.00 m directly in front of one of the speakers. Consider the audible range for normal hearing, 20 Hz to 20 kHz.(a)

(a) What is the lowest frequency that gives minimum signal (destructive interference) at the listener's ear?
__Hz

(b) What is the second lowest frequency that gives minimum signal?
__Hz

(c) What is the third lowest frequency that gives minimum signal?
__Hz

(d) What is the lowest frequency that gives maximum signal (constructive interference) at the listener's ear?
__Hz

(e) What is the second lowest frequency that gives maximum signal?
__Hz

(f) What is the third lowest frequency that gives maximum signal?
__Hz

Explanation / Answer

a) the difference in distance to the listener is sqrt(3.10^2 + 2.30^2) - 3.1 = 0.76m b) minimum destructive interference occurs when d = ?/2 so ? = 2*d = 2*0.76 = 1.52m so f = c/? = 343/1.52 = 226Hz c) the next frequency is d = 3?/2 so ? = 2*d/3 = 2*0.76/3 = 0.5067m so f = c/? = 343/0.5067 = 677Hz d) constructive interference occurs at d = ? = 0.76m f = c/? = 343/0.76 = 451Hz

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