Question

At a point 13.0 m from a source of spherical sound waves, you measure a sound intensity of 790 mW/m2 . How far do you need to walk, directly away from the source, until the intensity is 220 mW/m2

Answer 1

Answer:

11.6 m

Explanation:

The intensity of sound is inversely proportional to the square of the distance from the source. If we denote intensity with I and distance with d,

$I \propto \dfrac{1}{d^2}$

This can be resolved for any two situations as

$I_1d_1^2 = I_2d_2^2$

$d_2 = d_1\sqrt{\dfrac{I_1}{I_2}}$

$d_2 = 13\sqrt{\dfrac{790}{220}} = 24.6$

Therefore, you need to walk 24.6 - 13 m = 11.6 m away from the source.