Two speakers emit coherent sound waves into the open air.One of them produces 75 W of power.If a microphone placed at 12 m from each of the two speakers receives a total intensity of 0.25 W/m²,what is the power output of the second speaker? A) 151 W B) 377 W C) Need more info to solve. D) 38 W

Question

Quizplus · Accepted Answer

The total intensity received by the microphone is the sum of the intensities of the sound waves from the two speakers. Since the waves are coherent, their amplitudes add up, so the total intensity is proportional to the sum of the squares of their amplitudes. 
Let A be the amplitude of the sound wave from the first speaker, and B be the amplitude of the sound wave from the second speaker. Then the power output of the first speaker is:
P1 = IA^2, where I is the intensity per unit area at a distance of 12 m.
We can find I from the total intensity:
0.25 W/m^2 = I(A^2 + B^2)
0.25 W/m^2 = I(75^2 + B^2)
I = 0.25/(75^2 + B^2)
The power output of the second speaker is:
P2 = IB^2 = I(0.25 W/m^2 - P1) = I(0.25 W/m^2 - 75 W)
Substituting for I and solving for B, we get:
B = sqrt(0.25/(75^2 + 0.25 - 75)) = 0.00754 W/m^2
Therefore, P2 = IB^2 = 377 W.

Two Speakers Emit Coherent Sound Waves into the Open Air