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're sitting? What are the two lowest frequencies for which the volume will be the quietest? The speed of sound in the air in the room is 343 m/s; ignore wall, ceiling and floor reflection interference. Assume your cars are equally responsive to the volume level of ail frequencies.

Explanation / Answer

Formu for Youngs Modulus Y = FL/ A * dL

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

then the waves reach the observer in phase and interfer constructively.- loud

so L = 2.45

and 2L = 2.45

use the relation V = Lf

where f is frequecy

V is velcoity

so frequency is f1= V/ lambda

f1 = 343/2.45 = 140Hz

and

f2= V/ lambda =

f2 = 343/1.225

f2 = 280Hz

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

so 2.45 = L/2

and 2.45 = 3L/2

for two quiet cases.

so frequency is f1= V/ lambda

= 343/4.9 = 70Hz and

f2= V/ lambda

f2 = 343/1.633

f2 = 210Hz

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