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

Thanks!

Explanation / Answer

we use the relationship I = P/A, and area ( of a sphere ) is 4?r2

The 4? is constant in all scenerios, so we actually only need to look at I ? P/r2. This is Iold.

1. The power is 1/4, and the d is closer by 2, so numerator 1/4 smaller, but denominator is 2 times closer, but SQUARED, so denominator is 1/4.

Inew = ( 1/4 )P/( 1/4)r2, so the final answer is simply I ? P/r2, or Inew = Iold

2. Now, instead of 1/4 in the denominator, it is 4 in the denominator, so:

Inew = ( 1/4 )P/( 4 )r2 the final answer is Inew ? ( 1/16)Iold

3. Inew = ( 3 )P/( 9 )r2 the final answer is Inew ? ( 1/3)Iold

4. simply Iold

5. Inew = ( 4 )P/( 4 )r2 the final answer is Inew = Iold

1,4 and 5 are all equal, so I am not sure how they want you to answer, but from smallest to largest:

2, 3, 1=4=5

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