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?

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

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

You are correct, the equation I2/I1 = (r1/r2)^2 is the correct equation to use for this situation. However, the value you choose for I2 does matter and can affect the result.

Here's how to correctly use the equation:

1. Start by writing down the given information:
- Initial intensity (I1) = 4*10^-2 W/m^2
- Final intensity (I2) = 3*10^-6 W/m^2
- Initial distance (r1) = 10 m

2. Plug the values into the equation I2/I1 = (r1/r2)^2 and solve for r2:
(3*10^-6)/(4*10^-2) = (10/r2)^2

3. Rearrange the equation to solve for r2:
(3*10^-6)/(4*10^-2) = 1/(r2^2)
(3*10^-6)*(r2^2) = 4*10^-2
r2^2 = (4*10^-2)/(3*10^-6)
r2^2 = (4*10^-2)*(1/(3*10^-6))
r2^2 = 4/3
r2 = √(4/3)

4. Calculate the value of √(4/3):
r2 ≈ √(4/3) ≈ 1.1547

Therefore, the construction worker needs to move approximately 1.1547 meters away from the sound source to reach an intensity of 3*10^-6 W/m^2.

If you got different answers when plugging in different values for I2, make sure you're using the correct equation and double-check your calculations.