Answer Calculation of Sound Intensity and Power Output

[Noir]

Homework Statement

What is the sound intensity 2.5m away from a 50W speaker? (Assume sound is spread out in a sphere) The intensity level 12.0m from a loudspeaker, placed out in the open, is 100 dB, what is the acoustic power output (in Watts) of the speaker?

Homework Equations

$$I =10^{\frac{B}{10} - 12}$$

$$v =\frac{P}{A}$$

The Attempt at a Solution

I = P / A
I = 50 / (4 * pi * 2.5 ^ 2)
I = 0.64 W / m ^ 2

If the inensity level is 100 dB, then the Sound intensity is 10 ^ -2 W / m ^ 2.
So, If I = P / A
I x A = P
P = 10 ^ -2 x (4 * pi * 144)
P = 18.2 Watts

Is this correct? The 18.2 Watts looks a little for a speaker putting out 100 dB at 12 m...

 

[Redbelly98]

Looks good.

Note that the 50W speaker produces between 110 and 120 dB at 2.5 m, so 100 dB for 18 W is not out of line.