How Do Distance and Power Affect Sound Intensity Levels?

[Triathlete]

Second problem of the day...

Homework Statement

(part 1 of 2)
A spherical source radiates sound uniformly
in all directions. At a distance of 52 m, the
sound intensity level is 46 dB.
At what distance from the source is the
intensity level 13 dB?
Answer in units of m

(part 2 of 2)
What power is radiated by this source?
Answer in units of W

Homework Equations

I = P/A

A = 4[itex]\pi[/itex]r²

The Attempt at a Solution

I got part 1, which is 2322.8 m. But I'm not sure where to go from here. All I know is I need to solve for P in the equation but I'm not sure what to do for I.

 

[jbsteele]

Any help would be appreciated. For part 1, you can use the inverse-square law of sound. This states that the intensity of a sound source is inversely proportional to the square of the distance from the source. That is, the intensity I at a distance d from the source is related to the intensity I0 at a distance d0 from the source by I = I0 x (d0/d)2. Using this equation, we can solve for d0 when we know I0 and d. We have I0 = 46 dB, and d = 52m. Plugging these values into the equation, we have d0 = 2322.8m. For part 2, we can use the equation I = P/A, where P is the power radiated by the source, and A is the surface area of the sphere. Since the sound is radiating in all directions, the surface area of the sphere is 4πr2. We know the intensity I is 46 dB, so we can solve for P by plugging in these values. We get P = 4π(52)2 x 46dB = 7.67 x 106 W.