Help with a Wave Intensity Problem

[Smx_Drummerboy]

[SOLVED] Help with a Wave Intensity Problem

Hello all, here is a problem that relates to Wave Motion, more specifically Wave Intensity I believe:

The figure shows two observers 20m apart on a line that connects them and a spherical light source.
Figure: (The best I know to do)

(Person A)<----------20m----------->(Person B)<----------?m---------->(Light Source)

If the observer nearer the source measures a light intensity 45 % greater than the other observer, how far is the nearer observer from the source?

Relevant Equations:
I = [ latex ] \frac{P}{(4pi(r^2))} [ /latex ]

My initial thought was to state the following:
Ia = .45Ib and da = x +20 and db = x

Then plug in all the values given, the P's cancel, and I thought I'd be left with an answer. I got 41m, apparently that isn't right. I've been working on this problem for nearly an hour and a half.

Any suggestions?

 

[member 553083]

Solution:We can use the intensity equation given to solve for the distance.Ia = .45Ib [latex]\frac{P}{(4\pi (d_a^2))}[/latex] = .45[latex]\frac{P}{(4 \pi (d_b^2))}[/latex] Cross multiplying and simplifying, we get:[latex]d_a^2 = 0.45d_b^2+20^2[/latex] Solving for d_a, we get:[latex]d_a = \sqrt{0.45d_b^2+20^2}[/latex] Substituting db = 20m and solving, we get:[latex]d_a = \sqrt{0.45(20^2)+20^2}[/latex] [latex]d_a = 22.4m[/latex] Therefore, the observer nearer to the source is 22.4m away from it.