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?

Question

asked Aug 27, 2022 216k views

1 Answer

Blueling · Answer 1 · 2022-09-01T12:50:04+0000

Solution :

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
$3√(2)\ m$ .