Question

The intensity of a sound varies inversely with the square of its distance from the source. At a distance of 1 meter, the intensity of a jet engine noise is 10 watts per square meter. An airport cargo worker is 15 meters from the jet engine. What is the sound intensity at this distance?

Answer 1

The sound intensity at the distance of 15 meters is 0.044 watts.

Explanation:

Given as :

For the distance of 1 meter , the intensity of jet engine noise = 10 watts

∵ The intensity of sound is define as the power carried by sound waves per unit area in the direction perpendicular to that area

So , the intensity of sound is inversely proportional with square of distance

I.e
`I \propto (1)/(d^(2))` , where d is the distance

or,
`I = (k)/(d^(2))`

Now ,

∵ For 1 meter the intensity of sound is 10 watts

∴ Let for 15 meter the intensity of sound is
`I_2`

So ,
`(I_2)/(I_1) =( (d_1)/(d_2) )^(2)`

Or,
`(I_2)/(10) =( (1)/(15) )^(2)`

Or,
`I_2` =
`(1)/(225)` × 10 watts

∴
`I_2` = 0.044 watts

Hence The sound intensity at the distance of 15 meters is 0.044 watts. Answer