Two in-phase loudspeakers are 3.00 m apart. They emit sound with a frequency of 490 Hz. A microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of constructive interference is found. At what distance from that midpoint is that first point? The speed of sound in air is 343 m/s.
A) 0.175 m
B) 0.350 m
C) 0.500 m
D) 0.700 m
E) There is no point in that line where constructive interference occurs.

Question

Quizplus · Accepted Answer

First, we need to find the wavelength of the sound waves:

λ = v/f = 343 m/s / 490 Hz = 0.7 m

Next, we need to determine the path difference between the two speakers and the microphone for constructive interference to occur:

Δx = nλ/2, where n is an integer (1, 2, 3, ...)

At the midpoint between the speakers, the path difference is zero. As we move the microphone along the line joining the speakers, the path difference increases by λ/2 for each half-wavelength. The first point of constructive interference occurs when the path difference is equal to λ/2:

Δx = λ/2

nλ/2 = λ/2

n = 1

Therefore, the microphone must be located at a distance of 0.35 m from the midpoint between the speakers (halfway between them). This is because constructive interference occurs when the path difference between the two waves is an integer multiple of the wavelength.

Two In-Phase Loudspeakers Are 3