12.4 Two speakers are driven by the same amplifier and emit sinusoidal wves in p

Question

12.4 Two speakers are driven by the same amplifier and emit sinusoidal wves in phase. The speakers are on the x axis a distance d = 2.80 m apart. Th fequency 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) constuctive interference occur? (c) Can destructiv or constructiv interference occur at a point on the x axi 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

speed = 336 m/s

wavelength, w = 336/200 m = 1.68 m

a) when they are ((2n+1)/2)w apart (where n=0, 1, 2 ...), destructive interference occurs. hence the distances are 0.84m (n=0) and 2.52 m (n=1).

b) when they are (n)w apart (where n= 1, 2, 3 ...), constuctive interference occurs. hence the distances are 1.68 m (n=1).

c) Yes, to both the sides destructive or constructive interference can occur. the only thing that matters is path difference.

if the path difference is ((2n+1)/2)w apart (where n=0, 1, 2 ...), destructive interference occurs.

if the path difference is (n)w apart (where n= 1, 2, 3 ...), constuctive interference occurs

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