The ability to hear a “pin drop” is the sign of sensitive hearing. Suppose a 0.55-g pin is dropped from a height of 28 cm, and that the pin emits sound for 1.5s when it lands. Assuming all of the mechanical energy of the pin is converted to sound energy, and that

Question

The ability to hear a “pin drop” is the sign of sensitive hearing. Suppose a 0.55-g pin is dropped from a height of 28 cm, and that the pin emits sound for 1.5s 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. (The sound intensity at the threshold of hearing is Io = 10-12 W/m2.)

Chanz · Answer

I = P/4pi r^2 (for spherical dissipation) solve for r: r = sqrt(P/I4pi) In this case power is given by mgh/t. Watch your units, kg and m only.