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 your ear over a distance of 0.24 m. If the pulse has a sound level of 65 dB at your ear, find the rate at which energy is produced by the cavitation.

Please show your work.

Please calculate a final answer.

Explanation / Answer

This is problem includes: intensity, power, intensity level. You just have to connect all three. Note that they ask you to find "rate at which energy is produced", which is simply power.

So... power = intensity * area

The area in this case, since the power is transmitted uniformly in all directions, is that of a sphere: 4 pi r^2

Also, they give you the intensity level, 65 dB, which is related to the intensity:

intensity level = 10 log (intensity / Io )

where Io = 1x10-12

So now...     65 = 10 log (intensity / 1x10-12 )

        6.5 = log (intensity / 1x10-12 )

    106.5   = intensity / 1x10-12  

intensity = 3.162 x 10-5

Finally...

   power = intensity * area = 3.162 x 10-5 * 4 * 0.242= 2.29 x 10-6 Watts

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