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

Explanation / Answer

Here,

intensity is given as

I = Power/(4pi * d^2)

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

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

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

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

Power of speaker is 2P and distance to speaker is 2d.

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

Power of speaker is 4P and distance to speaker is 2d.

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

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

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

Now, giving ranks

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

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