When you \"crack\" a knuckle, you suddenly widen the knuckle cavity, allowing mo

Question

When you "crack" a knuckle, you suddenly widen the knuckle cavity, allowing more volume for the synovial fluid inside it and causing a gas bubble suddenly to appear in the fluid. The sudden production of the bubble, called "cavitation", produces a sound pulse---the cracking sound. Assume that the sound is transmitted uniformly in all directions and that it fully passes from the knuckle interior to the outside, at a distance of 0.31 m from your ear. If the pulse has a sound level of 62 dB at your ear, what is the rate at which energy is produced by the cavitation?

Explanation / Answer

given

at distance, d = 0.31 m

sound intensity level, beta = 62 dB

let I is the intensity of sound wave at the your location.

Apply,

sound intensity level, beta = 10*log(I/Io)

60 = 10*log(I/10^-12)

6 = log(I/10^-12)

10^6 = I/10^-12

I = 10^(6 - 12)

= 10^-6 W/m^2

now Apply, Intensity = Power/Area

==> Power = Intebsity*Area

= 10^-6*4*pi*0.31^2

= 1.21*10^-6 W/m^2

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