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 10⁸ 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/4πr².)