Cracking Your Knuckles When you \"crack\" a knuckle, you cause the knuckle cavit

Question

Cracking Your Knuckles When you "crack" a knuckle, you cause the knuckle cavity to widen rapidly. This, in turn, allows the synovial fluid to expand into a larger volume. If this expansion is sufficiently rapid, it causes a gas bubble to form in the fluid in a process known as cavitation. This is the mechanism responsible for the cracking sound. (Cavitation can also cause pits in rapidly rotating ship's propellers.)

If a "crack" produces a sound with an intensity level of 55 dB at your ear, which is 15 cm from the knuckle, how far from your knuckle can the "crack" be heard? Assume the sound propagates uniformly in all directions, with no reflections or absorption.

Explanation / Answer

Intensity of sound at a point where intensity level is 55dB can be found by

55 = 10 log I/I (I = 10^-12 )

So I/ I = 3.15*10^5

Intensity of sound is inversely proportional to square of distance from the source

So square root (,/ ) of I/ I =d / d

d = ,/3.15*10^5 × 0.15

= 84.6 m

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