When a pin of mass 0.120 g is dropped from a height of 1.30 m, 0.05% of its ener

Question

When a pin of mass 0.120 g is dropped from a height of 1.30 m, 0.05% of its energy is converted into a sound pulse with a duration of 0.1 s. For both questions below, assume that the intensity is I=P/4PIr^2
(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.

Explanation / Answer

m = 0.120 g, h = 1.30 m, t = 0.1 s
energy = mgh
sound energy E = 0.05%mgh
power P = E/t = 0.05%mgh/t
intensity I = P/(4r2)

so r = [P/(4I) = [0.05%mgh/(4It) = 7.80*10-4/I

(a) I = 10-11 W/m2, r = 247 m
(b) I = 10-8 W/m2, r = 7.8 m

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