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

E = m g h = 0.6E-3 9.81 0.3 = 1.76 mJ

Emitting this in 1.5 ms gives 0.50 W.

ntensity level (SIL) of 1 pW/m^2 is often considered the reference level we have to calculate the distance at which this level is reached. Since the surface area over which the sound spreads is have a sphere we find:

1E-12 = 0.50 / (2 pi r^2) => r = sqrt(0.50/(2E-12 pi)) = 287.7 km

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