A microphone records sound produced from two speakers. As the microphone is moved around, a position at which the microphone receives a minimum intensity is found. If the intensity of one of the sound waves alone at that location is 0.055 W/m², and if the microphone receives an intensity of 0.004 W/m² there, what is a possible value for the intensity of the other source at the microphone's location? A) Need more info to solve. B) 0.089 W/m² C) 0.051 W/m² D) 0.048 W/m²

Question

Quizplus · Accepted Answer

According to the principle of superposition, the total intensity at the position of minimum intensity is the sum of the individual intensities of each source. Let I1 be the intensity of one speaker and I2 be the intensity of the other speaker. Then we have:
I1 + I2 = 0.004 W/m^2 (1)
And at the location of minimum intensity, the intensity due to one source alone is:
I1 = 0.055 W/m^2 (2)
Substituting (2) into (1), we get:
0.055 W/m^2 + I2 = 0.004 W/m^2
Solving for I2, we get:
I2 = 0.004 W/m^2 - 0.055 W/m^2 = -0.051 W/m^2
Since intensity is a positive quantity, this means that the two sources are actually out of phase at the location of minimum intensity. However, we are asked for a possible value of the intensity of the other source, so we take the absolute value and get:
|I2| = 0.051 W/m^2
Therefore, the answer is B.

A Microphone Records Sound Produced from Two Speakers