The loudness of a sound is inversely proportional to the square of your distance from the source of the sound. if your friend is right next to the speakers at a loud concert and you are four times as far away from the speakers, how does the loudness of the music at your position compare to the loudness at your friend's position?

Question

Physics

Karter Randall

23 March, 00:26

The loudness of a sound is inversely proportional to the square of your distance from the source of the sound. if your friend is right next to the speakers at a loud concert and you are four times as far away from the speakers, how does the loudness of the music at your position compare to the loudness at your friend's position?

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Answers (1)

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Skylar Daugherty · Answer 1

Let loudness be L, distance be d, and k be the constant of variation such that the equation that would best represent the given above is,

L = k / (d^2)

For Case 1,

L1 = k / (d1^2)

For Case 2,

L2 = k / ((d1/4) ^2)

For k to be equal, L1 = 16L2.

Therefore, the loudness at your friend's position is 16 times that of yours.