Question

A construction worker needs to move away from a sound source which is 10m away. If the intensity at that distance is 4*10^-2 W/m^2 and they want to move to make it 3*10^-6 W/m^2, how far away do they have to move?

I'm using the equation I2/I1=(r1/r2)^2, but I'm getting different answers depending on which value I plug in as I2, this doesn't seem right because it shouldn't really matter, should it?

Answer 1

you are decreasing the power by a factor of 4E-2/3E-6=1.33 E4, so you should move it by a factor of sqrt(1.33E4) meters, so the new distance is 1000sqrt1.33

With your method, I2/I1 = .75E-4, so

sqrt(.75E-4)=10/r2 or

r2= 10/sqrt (.75E-4) or 1000/sqrt.75

Answer 2

oh, okay, I see; thank you very much.