Question

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

Answer 1

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).