The ability to hear a \"pin drop\" is the sign of sensitive hearing. Suppose a 0

Question

The ability to hear a "pin drop" is the sign of sensitive hearing. Suppose a 0.57-g pin is dropped from a height of 21 cm, and that the pin emits sound for 2.5 ms when it lands. Assuming all of the mechanical energy of the pin is converted to sound energy, and that the sound radiates uniformly in all directions, find the maximum distance from which a person can hear the pin drop. (This is the theoretical maximum distance, but atmospheric absorption and other factors will make the actual maximum distance considerably smaller.)

_______m

Explanation / Answer

Mass of pin m = 0.57 g = 5.7 x 10-4 kg

Height from which pin was dropped h = 21 cm = 0.21 m

Time for which the sound is emitted = 2.5 ms = 2.5 x 10-3 s

Total energy before the dropping = total energy after the drop

sound energy = potential energy

sound energy = mgh = 5.7 x 10-4 x 9.8 x 0.21 = 1.173 x 10-3 J hearing theresold = 2 x 10-5 N/m2

sound energy emitted in a second is = (1.173 x 10-3) / ( 2.5 x 10-3) Js-1

= 0.4692 W

hearing theresold p = 2 x 10-5 N/m2 , density = 1.22 kg/m3 , A = 4r2  and speed c = 343 m/s

Power P = Ap2/c = 1.22 x 10-11 r2 W

Therefore

1.22 x 10-11 r2 = 0.4692

r = 1.9611 x 105 m Maximum distance upto which the pin drop sound can be heard.

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