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

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 $\dfrac{I_o}{2}$.

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

$\dfrac{I_o}{\dfrac{I_o}{2}} = \dfrac{d^2}{3^2}\\\\d^2 = 18 \\\\d = 3\sqrt{2}\ m$

Therefore, intensity will be halved at a distance of $3\sqrt{2}\ m$.