3. 6 points My Notes Ask Your Teacher In the figure, two speakers separated by d

Question

3. 6 points My Notes Ask Your Teacher In the figure, two speakers separated by distance di-1.90 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 d2 3.20 m directly in front of one speaker. Consider the full audible range for normal hearing, 20 Hz to 20 kHz and use 343 m/s for the speed of sound in air. d Speakers Listener (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

the difference in distance to the listener is sqrt(3.20^2 + 1.90^2) - 3.2 = 0.5216m

a) minimum destructive interference occurs when d = w/2 so w = 2*d = 2*0.5216 = 1.04m

so f = c/w = 343/1.04 = 328.82Hz

b) the next frequency is d = 3w/2 so w = 2*d/3 = 2*0.5216/3 = 0.3477m

so f = c/w = 343/0.3477 = 986.39Hz

c) the next frequency is d = 5w/2 so w = 2*d/5 = 2*0.5216/5 = 20864m

so f = c/w = 343/0.20864= 1643.98Hz

d) constructive interference occurs at d = w = 0.5216m

f = c/w = 343/0.5216 = 657.59Hz

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