Subjective Type

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 if fully passes from the knuckle interior to the outside. If the pulse has a sound level of 62 dB at your ear, estimate the rate at which energy is produced by the cavitation.

Solution

We use $$\beta = 10 \log \left (I/I_0 \right )$$ with $$I_0 = 1 \times 10^{-12} \space W/m^{2}$$ and $$I = P/4 \pi r^{2}$$ (an assumption we are asked to make in the problem).
We estimate $$r \approx 0.3 \space m$$ (distance from knuckle to ear and find
$$P \approx 4 \pi \left (0.3 \space m \right )^{2} \left (1 \times 10^{-12} \space W/m^{2} \right ) 10^{6.2} $$
$$= 2 \times 10^{-6} \space W = 2 \mu W$$.

SIMILAR QUESTIONS

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For a wave $$y=0.0002\sin \left[2\pi \left(110t-\dfrac{x}{3}\right)+\dfrac{\pi}{3}\right]$$ is travelling in a medium. The energy per unit volume being transferred by wave if density of medium is $$1.5\ kg/m^3$$, is :

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A transverse sinusoidal wave is generated at one end of a long, horizontal string by a bar that moves up and down through a distance of $$ 1.00 \mathrm{cm} . $$ The motion is continuous and is repeated regularly 120 times per second. The string has linear density 120 $$ \mathrm{g} / \mathrm{m} $$ and is kept under a tension of $$ 90.0 \mathrm{N} $$. What is the minimum rate of energy transfer along the string ?

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Energy is transmitted at rate $$ P_{1} $$ by a wave of frequency $$ f_{1} $$ on a string under tension $$ \tau_{1} . $$ What is the new energy transmission rate $$ P_{2} $$ in terms of $$ P_{1}$$, if the tension is increased to $$ \tau_{2}=4 \tau_{1} $$

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Energy is transmitted at rate $$ P_{1} $$ by a wave of frequency $$ f_{1} $$ on a string under tension $$ \tau_{1} . $$ What is the new energy transmission rate $$ P_{2} $$ in terms of $$ P_{1}$$, if , instead, the frequency is decreased to $$ f_{2}=f_{1} / 2 ? $$

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