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 0.45 g pin is dropped from a height of 29 cm , and that the pin emits sound for 1.5 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

We know that mechanical energy is given by:

E = m*g*h = 0.45*10^-3*9.81*29*10^-2

E = 1.28*10^-3 J

Now Power will be

P = E/t = 1.28*10^-3/1.5

P = 8.53*10^-4 W

Maximum distance where person can hear pin drop will be

Intensity = P/(4*pi*r^2)

Threshold intensity at max distance will be = I0 = 10^-12 W/m^2

So,

r = sqrt (P/(4*pi*I0))

r = sqrt (8.53*10^-4/(4*pi*10^-12))

r = 8238.91 m

r = 8.24 km

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