A microphone records sound produced from two speakers in a room with no other so

Question

A microphone records sound produced from two speakers in a room with no other sound sources. If the intensity of one of the sound waves at a given location is 0.055 W/m^2 and if the microphone receives a minimum intensity of 0.004 W/m^2 when both speakers are active what is a possible value for the intensity of the other source at the microphone's location?
A) Needs more info to solve B) 0.088 W/m^2 C) 0.051 W/m^2 D) 0.048 W/m^2
Answer: B A microphone records sound produced from two speakers in a room with no other sound sources. If the intensity of one of the sound waves at a given location is 0.055 W/m^2 and if the microphone receives a minimum intensity of 0.004 W/m^2 when both speakers are active what is a possible value for the intensity of the other source at the microphone's location?
A) Needs more info to solve B) 0.088 W/m^2 C) 0.051 W/m^2 D) 0.048 W/m^2
Answer: B
A) Needs more info to solve B) 0.088 W/m^2 C) 0.051 W/m^2 D) 0.048 W/m^2
Answer: B

Explanation / Answer

given, intensity due to one speaker, I1 = 0.055 W/m^2
microphone minimum intensity, Imin = 0.004 W/m^2 ( when both sdpeakers are active)
now, let the intensity of the other speaker be I2
then at destructive interference
(sqroot(I1) - sqroot(I2))^2 = Imin = 0.004
so (sqroot(0.055) - sqroot(I2)) = 0.004^2
I2 = 0.05499 W/m^2

so the answer is option c) 0.051 W/m^2

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