Two loudspeakers on a concert stage are vibrating in phase. A listener is 45.9 m from...

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Two loudspeakers on a concert stage are vibrating in phase. Alistener is 45.9 m from the left speaker and 34.7 m from the rightone. The listener can respond to all frequencies from 20 to 20 000Hz, and the speed of sound is 343 m/s. What is the lowest frequencythat can be heard loudly due to constructive interference?

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3.7 Ratings (735 Votes)

Path difference of the two sound waves x = 45.9 m - 34.7m

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 11.2 m

speed of sound v = 343 m/s

the lowest frequency that can be heard loudly due toconstructive interference f = v / x

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =30.7 Hz

Since for constructive interference path difference isintegral multiple of wavelength

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