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).
12345 Power of speaker is P and distance to speaker is d.
12345 Power of speaker is (1/9)P and distance to speaker is (1/3)d.
12345 Power of speaker is (1/9)P and distance to speaker is 3d.
12345 Power of speaker is 4P and distance to speaker is 2d.
12345 Power of speaker is 2P and distance to speaker is 2d.

Explanation / Answer

The sound intensity decreases with distance to source. Intensity and distance can be expressed as:

I = Pi/4*?*r^2

where:

Pi = sound power (W)

? = 3.14

r = radius or distance from source (m)

Rank:3<5<1=2=4

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

P/d^2

2)Power of speaker is (1/9)P and distance to speaker is (1/3)d.

(3*3)P/(9)d^2 = P/d^2

3)Power of speaker is (1/9)P and distance to speaker is 3d

P/(9*9)d^2 = 1/81P/d^2

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

4P/4d^2 = P/d^2

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

2P/4d^2 = 1/2(P/d^2)

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