Energy Output. By measurement you determine that sound waves are spreading out equally in all directions from a point source and that the intensity is 0.026 W/m2 at a distance of 4.3 m from the source. (a) What is the intensity at a distance of 3.1 m from the source? (b) How much sound energy does the source emit in one hour if its power output remains constant?

Solution 27E Step 1: Power related to intensity at distance r is given by P = I(4r )2 Energy is power times time. 2 Apply (r /1 )2= I /I1 2 Step 2: (a).The intensity at a distance of 3.1 m from the source is I r 2 = I r 2 1 1 2 2 2 I2= (r 2r )1I 1 I = (0.026 W/m )(4.3 m /3.1 m) 2 2 2 I2= 0.050 W/m