Two loudspeakers are placed next to each other and driven by the same source at 460 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. )

Question

Quizplus · Accepted Answer

To create constructive interference, the distance between the two speakers should be equal to an integer multiple of half of the wavelength of the sound. Here, the frequency is given as 460 Hz. Therefore, the wavelength of sound, λ = v/f = 340/460 = 0.739 m.
For constructive interference, the distance between the two speakers should be an integer multiple of λ/2 = 0.3695 m. 
For destructive interference, the distance between the two speakers should be an odd multiple of λ/4 = 0.1848 m (since there is a half-wavelength difference between the two paths to the listener). 
Moving one of the speakers backwards by this distance produces destructive interference. Therefore, the minimum distance one of the speakers should be moved back is 0.1848 m or approximately 0.37 m (Option C).

Two Loudspeakers Are Placed Next to Each Other and Driven