Problem
When a pin of mass 0.1 g is dropped from a height of 1 m, 0.05% of its energy is converted into a sound pulse with a duration of 0.1 s.
(a) Estimate the range at which the dropped pin can be heard if the minimum audible intensity is 10 -11 W/m2 .
(b) Your result in (a) is much too large in practice because of background noise. If you assume that the intensity must be at least 10-8 W/m2 for the sound to be heard, estimate the range at which the dropped pin can be heard. (In both parts, assume that the intensity is P/4?r2 .)
(a) Sound energy is 5 x 10-4 (mgh) = 5 x 10-4 (1m)(10-4 kg)(9.8 m/s2 ) = 4.9 x 10-7 J
Pav = E/?t = 4.9 x10-6 W = 4?r2 x10-11 W => r ~ 200 m.
(b) r ~ 200/ (1000)1/2 = 6.24 m.