Question

Two speakers face each other, and they each emit a sound of wavelength (lambda). One speaker is 180 (degrees)

%u2218out of phase with respect to the other. If we separate the speakers by a distance1.5 (lambda)
,how far from the left-most speaker should we place a microphone in order to pick up the loudest sound? Ignore reflections from nearby surfaces. Select all that apply.


A. 3/4 lambda
B. 0 lambda
C. 1/2 lambda
D. 1/4 lambda
E. 1 lambda

Answer 1

D. 1/4 lambda

Step-by-step explanation:

Given:

Initially out of phase speakers by 180°.

Then on being separated by 1.5 λ.

The initial case of speakers being out of phase by 180°

• In such a case we obtain destructive interference because the vectors of the waveform are equal and opposite in direction so they cancel out each other.

On separating the speakers by a distance of 1.5 λ.

• We obtain that the waves-forms are in-phase and form constructive interference leading to the highest value at the crest of the wave pattern, i.e. we obtain the loudest sound when we place a microphone at a distance of one-fourth of the wavelength.