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

11.6 m

Step-by-step 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 (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{(I_1)/(I_2)}`

`d_2 = 13\sqrt{(790)/(220)} = 24.6`

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