Two loudspeakers are placed next to each other and driven by the same source at 500 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)1.36 m
B)0.68 m
C)0.34 m
D)0.17 m

Question

Quizplus · Accepted Answer

Constructive interference occurs when two waves meet with the same phase, resulting in an increase in amplitude. Destructive interference occurs when two waves meet with opposite phases, resulting in a decrease in amplitude.

At the listener's ear, the two speakers are producing sound waves that interfere constructively. The distance between the two speakers and the listener is equal to half the wavelength of the sound wave, as this distance results in the two waves being in phase at the listener's ear.

For destructive interference to occur, the distance between the two speakers needs to result in the two waves being out of phase by half a wavelength at the listener's ear. To achieve this, one of the speakers needs to be moved back by a distance equal to a quarter of the wavelength.

We can use the formula: wavelength = speed of sound / frequency

wavelength = 340 m/s / 500 Hz = 0.68 m

Moving one of the speakers back by a quarter of the wavelength gives a distance of 0.17 m. Therefore, the answer is choice C.

Two Loudspeakers Are Placed Next to Each Other and Driven