Part lI:Calculations 3.00m 11. Two Loudspeakers, A and B, are driven by the same

Question

Part lI:Calculations 3.00m 11. Two Loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 3.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 214 Hz. Consider a point P between the speakers and along the line connecting them,a distance x to the right of A. Both speakers emit sound waves that travel directly from the speaker to point P. Assume speed of sound in air is 343 m/s. a. (5 points) Determine the values of x that will produce destructive interference at P between the two speakers b. (5 points) Determine the values of x that will produce constructive interference at P between the two speakers c. (10 points) The frequency is gradually increased above 214 Hz. At what next frequency above 214 H will there be destructive interference at point Q?

Explanation / Answer

distance traveleld by wave from speakerB r2 = d - x = 3-x

fordestructive interference path difference = m*lambda/2

m = 1 , 3, 5, ....

lambda = v/f = 343/214

r2 - r1 = 3-x

3 - x - x = m*343/(214*2)

3 - 2x = m*0.8

for m = 1

3-2x = 0.8

x = 1.1 m

for m = 3

3 - 2x = 3*0.8

x = 0.3 m

at x = 0.3 there is destrucitve interference

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(b)

for constructive interference path difference = m*lambda

3 -2x = m*1.6

m = 1, 2 , 3, 4 .......

for m = 1

3 - 2x = 1*1.6

x = 0.7 m

for x = 0.7 m   constructive interferenc takes place

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(c)

path difference at point Q = 4 - 3 = 1 m

for constructive interference

path difference = m*lambda/2 = m*v/(2f)

1 = 1*343/(2*f)

frequency f = 171.5 Hz

for m = 3

1 = 3*343/(2*f)

f = 514.5 Hz <<<<------ANSWER

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