[SOLVED] sound intensity - the threshold of pain

clope023

1. The problem statement, all variables and given/known data

You are investigating the report of a UFO landing in an isolated portion of New Mexico, and encounter a strange object that is radiating sound waves uniformly in all directions. Assume that the sound comes from a point source and that you can ignore reflections. You are slowly walking toward the source. When you are 7.5 m from it, you measure its intensity to be 0.11 W/m^2.

An intensity of 1.0W/m^2 is often used as the "threshold of pain". How much closer to the source can you move before the sound intensity reaches this threshold?

2. Relevant equations

I1/I2 = r2^2/r1^2

3. The attempt at a solution

r2 = r1(I1/I2)^1/2

= (7.5)(.11)^1/2 = 2.5m - incorrect

done another way

r2 = [(r1)^2(I1/I2)]^1/2 = (56m^2(.11))^1/2 = 2.5m - incorrect

I dont' know the equations aren't working for me, any help is appreciated.

Dick

You are doing the right thing. I get 2.48m. All I can think of is to check the number of significant figures they (or it) are expecting. Also note that the question is asking 'how much closer can you get'. Maybe they want you to say 5m closer?

clope023

yeah that was it apparently, the distance to obtain an intensity of 1W/m^2 is 2.5m and the intensity of .11W/m^2 was 7.5 so you travel 5 more meters to get within 2.5m of the threshold of pain's intensity, thanks for the hint.