Does sound gets faster when air bubble is suspend in water?
c = sqrt(K/P)
c = speed
K = bulk module
P = density
When air bubbles is homogenized into water the density is lower, so should sound gets faster? Thank you.
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For many small bubbles in water distributed homogeneously, as in the hot chocolate effect, the speed of sound decreases because the density only decreases slightly while the bulk modulus decreases dramatically (because most of the squeezing is done on the air in the bubbles, not the water). By "small" I mean small as compared to the wavelength of the sound. For audible sound this can be as small as 1 cm for 34kHz, and since most bubbles will be this size or less, then the reasoning above should be valid. (For something nonhomogeneous, like a single bubble in a container of water much longer than the sound wavelength, then we'd have the speed of sound be slower near the bubble and faster away from it.)
The mathematical details are listed here (behind paywall): http://dx.doi.org/10.1119/1.13080