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 0.54-g pin is dropped from a height of 25 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.)

Explanation / Answer

Potential Energy, PE = mgh = 0.54*10-3*9.8*25*10-2

PE = 1.323*10-3 J

Power = workdone / time

Power, P = 1.323*10-3/2.5*10-3 = 0.5292 Watt

power in dB = 10*log[0.5292 Watt*1012] = 117.2362 dB

0 - 117.2362 + 10log(4pi) = - 106.2441

-106.2441 = -20log(distance)

log(distance) = 5.3122

distance = 105.3122 = 205.21 km

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