You are sitting in a lecture hall where the physics instructor can play a single

Question

You are sitting in a lecture hall where the physics instructor can play a single tone (frequency) through two speakers. You happen to be sitting in a location where you are 8.75 m from one of the speakers and 6.30 m from the other speaker. The two speakers are in-phase with each other. If the instructor starts at a low (but still audible) frequency and slowly increases the frequency to higher and higher pitches, what are the two lowest frequencies for which the volume will be the loudest where you

Explanation / Answer

The difference in the path is r = 8.75m - 6.3m = 2.45m

When the path difference is either zero or integral multiple of the wavelength the two waves reach the observer in phase and interfer constructively.- loud

so 2,45 = lambda & 2.45 = 2 (lambda) for two loud cases.

so frequency is f1= V/ lambda = 343/2.45 = 140Hz and f2= V/ lambda = 343/1.225 = 280Hz

When the path difference half integral multiple of the wavelength the two waves reach the observer in phase and interfer destructive.- quiet

so 2,45 = lambda/2 & 2.45 = 3 (lambda)/2 for two quiet cases.

so frequency is f1= V/ lambda = 343/4.9 = 70Hz  and f2= V/ lambda = 343/1.633 = 210Hz

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