Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal

Question

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 218 Hz. Consider Point P between the speakers and along the line connecting them, a distance x to the right of speaker A. Both speakers emit sound waves that travel directly from the speaker to point P.

a) For what values of x will destructive interference occur at point P?

b) For what values of x will constructive interference occur at point P?

c) Can destructive or constructive interference occur at point Q? Explain.

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 218 Hz. Consider Point P between the speakers and along the line connecting them, a distance x to the right of speaker A. Both speakers emit sound waves that travel directly from the speaker to point P. a) For what values of x will destructive interference occur at point P? b) For what values of x will constructive interference occur at point P? c) Can destructive or constructive interference occur at point Q? Explain.

Explanation / Answer

wavelength lambda = L = v/f = 340/218 = 1.56 m

part a)

path difference = (2-x)-x = 2-2x = nL

2*(1-x) = n*1.56 m

if n = 1

x = 0.22 m <<<<----------answer

+++++++

part b)

path difference = n(L/2)

2*(1-x) = n*0.78

if n= 1

x = 0.61 m <-----answer

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