Question

The ability to hear a "pin drop" is the sign of sensitive hearing. Suppose a 0.50 g pin is dropped from a height of 27 cm, and that the pin emits sound for 1.4 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.)

Answer 1

Energy release = mgh = 1.32*10^-3 J
Avg. sound power = mgh/1.4s
= 0.95*10^-4 Watts

Avg. Sound intensity at distance R
= 0.95*10^-4 Watts/(4*pi*R^2)
= 7.5*10^-6/R^2 W/m^2

Set this equal to the minimum sound intensity level detectable by the human ear (about 10^-12 W/m^2), and solve for R.

Answer 2

should be 7.5*10^-5/R^2 W/m^2