Suppose a speaker is sending out a signal of a given power uniformly in all dire

Question

Suppose a speaker is sending out a signal of a given power uniformly in all directions. You are located a certain distance from the speaker measuring the intensity of the sound. Given the following different situations, rank the measured intensity (1 = the lowest intensity).
Power of speaker is (1/4)P and distance to speaker is (1/2)d.
Power of speaker is 3P and distance to speaker is 3d.
Power of speaker is 9P and distance to speaker is 3d.
Power of speaker is (1/4)P and distance to speaker is 2d.
Power of speaker is P and distance to speaker is d.

Explanation / Answer

Intensity = I = P/A = P/4*pi*d^2

Power of speaker is (1/4)P and distance to speaker is (1/2)d.

I1 = P/4*4*pi*(d/2)^2 = P/4pid^2 = I

Power of speaker is 3P and distance to speaker is 3d.

I2 = 3P/4*pi*(3d)^2 = P/4*pi*3*d^2 = I/3

Power of speaker is 9P and distance to speaker is 3d.

I3 = 9P/(4*pi*9d^2) = I

Power of speaker is (1/4)P and distance to speaker is 2d.

I4 = P/4(4*p*4d^2) = I/8

Power of speaker is P and distance to speaker is d.

I5 = P/4pid^2 = I

I5 < I2 < I1 = I3 = I5

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