Question

How many metres further would the sound intensity be 1/2 times as much as that at a distance of 3 m from an acoustic source?

Answer 1

Let, intensity at distance 3 m from the acoustic source is
`I_o`.

We need to find the distance d where the intensity is
`(I_o)/(2)`.

Now, we know intensity is inversely proportional to square of distance between the source.

`(I_o)/((I_o)/(2)) = (d^2)/(3^2)\\\\d^2 = 18 \\\\d = 3√(2)\ m`

Therefore, intensity will be halved at a distance of
`3√(2)\ m`.