72. Two point-source loudspeakers are a certaindistance apart, and a person stan

Question

72. Two point-source loudspeakers are a certaindistance apart, and a person stands 12.0 m in front of
      one of them on a line perpendicularto the baseline of the speakers. If the speakers emitidentical       1000-Hz tones,what is their minimum nonzero separation so that the observer hearslittle or no       sound? (Takethe speed to be exactly 340 m/s) 72. Two point-source loudspeakers are a certaindistance apart, and a person stands 12.0 m in front of
      one of them on a line perpendicularto the baseline of the speakers. If the speakers emitidentical       1000-Hz tones,what is their minimum nonzero separation so that the observer hearslittle or no       sound? (Takethe speed to be exactly 340 m/s)

Explanation / Answer

let the distance between the 2 be d so the path difference between the waves should be /2 =wavelength = c/f    f=frequency, c:speed of sound wave so path difference =d = /2 so d= 340/2000 = 0.17m there is one more case to this when the loudspeakers are on the opposite side of theman in this case the path difference is 12 + d mod(12-d) = /2 so mod(12-d)=0.17 so d=11.83 m (for min we take d<12) when the loudspeakers are on the opposite side of theman in this case the path difference is 12 + d mod(12-d) = /2 so mod(12-d)=0.17 so d=11.83 m (for min we take d<12)

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