Question

At 3.00 m from a source that is emitting sound uniformly in all directions, the sound level (b) is 60.0 dB.

How many meters from the source would the sound level be one-fourth the sound level at 3.00 m?

Answer 1

Given that,

At 3.00 m from a source that is emitting sound uniformly in all directions, the sound level is 60.0 dB.

To find,

The distance from the source would the sound level be one-fourth the sound level at 3.00 m.

Solution,

The intensity from a source is inversely proportional to the distance.

Let I₁ = 60 dB, r₁ = 3 m, I₂ = 60/4 = 15 dB, r₂ =?

Using relation :

`(I_1)/(I_2)=(r_2^2)/(r_1^2)\\\\r_2^2=(I_1r_1^2)/(I_2)\\\\r_2^2=(60* (3)^2)/(15)\\\\r_2=6\ m`

So, at a distance of 6 m the sound level will be one fourth of the sound level at 3 m.