Question

You stand 5 m from a trumpet player. If you then back up to 10 m,...

You stand 5 m from a trumpet player. If you then back up to 10 m, how many trumpet players (playing at an identical volume and distance from you) must play for you to hear the same sound level in both locations?

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Answer #1

Intensity of a sound produced follows the inverse square law. That means, as you move further, the intensity drops at the rate of square of the distance you have moved.

Let us assume that at 5 meters away the intensity we hear is, . So, at 10 meters, the intensity will drop by

So, the intensity will 4 times less, than then intensity at 5 meters. To hear the same sound 10 meters away, if we add to the initial intensity by having 4 instead of 1 trumpet players, the intensity 5 meters away will be . While the intensity at 10 meters will be,

So our answer is 4.

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