Find the distance from the source of power

[demonslayer42]

Homework Statement

A point source power outputs a power of 100 W. If a decibel reading of 118 dB is heard, what is the distance to the observer.

Homework Equations

I = P/(4*pi*r^2)

The Attempt at a Solution

This should be simple, but for some reason my numbers aren't matching up.

First I converted 118 dB to an intensity of .6309 w/m^2 Then I plug it back into the equation and solve for r which comes out to be 4.471 meters.

So then to check it I put the 4.471 m back into the equation to see if it equals my intensity which it doesn't. I'm not sure where I went wrong on this one. Any help would be greatly appreciated.

 

[JaredJames]

What are you using to convert dB to intensity? Are you using the log function correctly?

 

[demonslayer42]

Yes, I think so. 118 = 10 log (I/Io) Io = 10^(-12) so,
118 = 10 log (I/10^(-12))
11.8 = log (I/10^(-12))
10^(11.8) = (I/10^(-12)
I = 0.6309 w/m^2
Is that correct?

 

[JaredJames]

Yes, I think so. 118 = 10 log (I/Io) Io = 10^(-12) so,
118 = 10 log (I/10^(-12))
11.8 = log (I/10^(-12))
10^(11.8) = (I/10^(-12)
I = 0.6309 w/m^2
Is that correct?

Sorry, that seems fine. Read it wrong the first time.

 

[JaredJames]

Right, gone through it properly I get r = 3.55m.

Your values are correct, check how you re-arrange your equation.

I = P / (4*pi*r²)

(4*pi*r²) = P / I

r² = ((P / I) / 4*pi)

r = sqrt( (P/I) / 4*pi )

 

[demonslayer42]

omg, I feel so dumb lol yeah that's where I messed up. Instead of (P/I)/(4*pi) I did (P/I*4*pi). Thank you for your help :)