Question

The intensity of a certain siren is 0.060 W/m^2 from a distance of 25 meters. What is the intensity of this siren at a distance of 50 meters?

Answer 1

The intensity of siren is 0.015 W m⁻²

Explanation:

The intensity of sound is inversely proportional to the square of distance between source and the observer .

Thus Intensity at a distance 25 m  is I₁ ∝ $\frac{1}{r_1^2}$                               I

Similarly the intensity at a distance 50 m is I₂ ∝ $\frac{1}{r_2^2}$               II

Dividing II by I , we have

$\frac{I_2}{I_1}$ = $\frac{r_1^2}{r_2^2}$ = $\frac{25^2}{50^2}$ = $\frac{1}{4}$

Thus I₂ = $\frac{1}{4}$ x 0.06 =  0.015 W m⁻²