Two speakers emit incoherent sound waves into the open air. One of them produces 75W of power. A microphone is placed at a position that is 12m from each speakers, and it receives a total intensity of 0.25W/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

Intensity is given by I = P/(4πr^2), where P is the power and r is the distance from the source. 
Let P1 and P2 be the power outputs of speaker 1 and speaker 2 respectively. 
Given, P1 = 75W, r = 12m, and total intensity = 0.25W/m^2. 
Using the formula for intensity and simplifying, we get: 
0.25 = P1/(4πr^2) + P2/(4πr^2) 
0.25 = (75)/(4π(12^2)) + P2/(4π(12^2)) 
0.25 = 0.0492 + P2/(4π(12^2)) 
P2 = (0.25-0.0492)*(4π(12^2)) 
P2 = 376.8 W 
Therefore, the power output of the second speaker is approximately 377 W.

Two Speakers Emit Incoherent Sound Waves into the Open Air