Cracking Your Knuckles When you \"crack\" a knuckle, you cause the knuckle cavit
ID: 1470197 • Letter: C
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 58 dB at your ear, which is 18 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
SOLUTION =
0 dB is the threshold of hearing
the dB scale is defined by
dB = 10 log(I/I0) where I0=10^(-12) W/m^2 and is the threshold of hearing
so we want to figure out how far away you have to be so this intensity is 0dB or 10^(-12)W/m^2
58 dB has an intensity:
58=10log(I/10^(-12)) where I is the intensity of the crack and log is a base 10 log
5.8=log(I/I0)
10^(5.8)=I/10^(-12) =>I = 10^(-6.3)=5.01x10^(-7)
this intensity is 5.01x10(-7)/10^(-12) =5.01x10^5 times greater than the threshold intensity
since intensity of sound varies as 1/r^2, we need to move 708 times
farther away (since 5.01x10^5/708^2=1).
this means you can hear the sound 708x18cm=12744 cm or 127.44m away