Two loudspeakers are placed next to each other and driven by the same source at 515 Hz.A listener is positioned in front of the two speakers and on the line separating them,thus creating a constructive interference at the listener's ear.What minimum distance would one of the speakers be moved back away from the listener to produce destructive interference at the listener's ear? (The speed of sound = 340 m/s. )
A)1.5 m
B)0.66 m
C)0.33 m
D)0.17 m
E)3.0 m

Question

Quizplus · Accepted Answer

To create constructive interference at the listener's ear, the distance between the two speakers must be an integer multiple of the wavelength of the sound wave. Since the frequency of the source is 515 Hz, the wavelength can be calculated using the formula:

wavelength = speed of sound / frequency

wavelength = 340 m/s / 515 Hz ≈ 0.66 m

Thus, the distance between the two speakers must be an integer multiple of 0.66 m for constructive interference to occur at the listener's ear.

To produce destructive interference, one of the speakers must be moved back by half a wavelength, or 0.33 m. This will make the distance between the two speakers an odd multiple of the wavelength, resulting in destructive interference at the listener's ear. Therefore, the minimum distance that one of the speakers needs to be moved back is 0.33 m.

Hence, the answer is C) 0.33 m.

Two Loudspeakers Are Placed Next to Each Other and Driven