A listener increases his distance from a sound source by a factor of 4.49.

Assuming that the source emits sound uniformly in all directions, what is the change in the sound intensity level in dB?

Answer: Δβ (dB) = - 13.1dB

Explanation:

The intensity of sound is inversely proportional to the square of the distance between them.

I ∝ 1/r²

I₁/I₂ = r₂²/r₁² ... 1

When the listener increases his distance from the source by a factor of 4.49.

Then,

r₂/r₁ = 4.49

From equation 1

I₁/I₂ = (4.49) ²

I₁/I₂ = 20.16

I₂/I₁ = 1/20.16

The change in sound intensity in dB can be given as

Δβ (dB) = 10 log (I₂/l₁) = 10log (1/20.6) = - 13.1dB