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 0.60 g pin is dropped from a height of 25 cm , and that the pin emits sound for 1.7 s 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 ideal maximum distance, but atmospheric absorption and other factors will make the actual maximum distance considerably smaller.)

Explanation / Answer

given,

mass = 0.6 gm

height = 25 cm

time = 1.7 s

power = mgh / time

power = 0.6 * 10^-3 * 9.8 * 0.25 / 1.7

power = 0.000865 Watt

sound intensity level (SIL) of 1 pW/m^2 is often considered the reference level

so,

1 * 10^-12 = 0.000865 / (pi * r^2)

r = 0.000865 / (pi * 1 * 10^-12)

r = 16.593 km

maximum distance from which a person can hear the pin drop = 16.593 km

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