By what amount does the sound intensity decrease when the distance to the source doubles?

The relationship of the two is that, the sound intensity is inversely proportional to the square of the distance of the source.

I α 1 / r^2

Where I = intensity and r = distance from source

From this, we can equate two conditions 1 and 2:

I1 / I2 = r2^2 / r1^2

So when r2 = 2 r1, the intensity becomes:

I1 / I2 = (2r1 / r1)^2

I1 / I2 = 4

I2 = I1 / 4

So when we double the distance of the source, the intensity of the sound reduces by a factor of 4 (divided by 4).

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