Two speakers are driven by the same amplifier and emit sinusoidal waves in phase

Question

Two speakers are driven by the same amplifier and emit sinusoidal waves in phase. The speakers are on the x axis a distance d= 2.80 m apart. The frequency of the sound waves produced by the loudspeakers is 200 Hz. For a point on the x axis between the two speakers, at what values of x will (a) destructive interference occur, and b) constructive interference occur? (c) Can destructive or constructive interference occur at a point on the x axis to the right of both speakers or to the left of both speakers? Explain. [Assume the speed of sound is 336 m/s.]

Explanation / Answer

part a )

for destructive interferance

dx = (n+1/2)*lambda

dx = (n+ 1/2)*lambda

lambda = v/f = 336/200 = 1.68 m

n = 0

dx = 0.84 m

n =1

dx = 2.52 m

n = 2

dx = 4.2 m

in between there are two point = 0.84 m , 2.52 m

for constructive interference

dL = n*lambda

dL = lambda

dL = 1.68m

part c )

right of the both speaker

if you increase the value of n you will go towards right of x axis

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