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 0.60g pin is dropped from a height of 30cm , and that the pin emits sound for 1.5s when it lands.

Part A: 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 ideal maximum distance, but atmospheric absorption and other factors will make the actual maximum distance considerably smaller.)

Explanation / Answer

Energy = E = m g h = 0.60e-3 * 9.8 *0.30 = 0.001764 J

P = E/t = 0.001764/1.5 = 0.001176 Watts

I = P/A

==> A = P/I = 0.001176/1e-12 = 1.176e9 m2

A = 4 pi r^2

==> r = 9670 m

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