Question

The ability to hear a "pin drop" is the sign of sensitive hearing. Suppose a 0.63 g pin is dropped from a height of 27 cm, and that the pin emits sound for 1.3 s 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.)

Express your answer using two significant figures.

Answer 1

mgh = 0.00063 x 9.8 x 0.27 = 0.001668681 J

Power = work done/time

work done = 0.001668681 J

time = 1.3 secs

0.001668681/1.3 = 0.0012836 Watts

10log(0.0012836/10^(-12)) = 91.084 dB

0 - 91.084 + 10log(4pi) = -80.0922

-80.0922 = -20log(distance)

-80.0922/-20 = log(distance) = 4.0046

10^4.0046 = distance = 10106 m or 10.1 km

Of course all of the above is theoretical and WILL not happen in reality, for one the sound generated will not be even a fraction of the 91.084 dB (this is close to a rock concert) the sound would be more like some 18 dB and the rest of the energy converted into heat etc