Bubble Resonance

{image borrowed from: **www.fotosearch.com/ IGS347/is237-001/** }

Remember now that bubbles are governed by a function of pressure and surface tension, so what do

we expect to happen when a bubble is subjected to an external pressure variation? Let us consider

that some pressure wave (i.e. acoustic) propagates through an area where a bubble resides. We see

that this pressure difference induces a change in the radius of the bubble (remember radius is a

function of pressure). One expects that once the pressure variation has passed there will be a

restoring force acting to return the bubble to it's originol radius. There results from this a subsequent

radial oscillation in the bubble{8}. To one familiar with oscillators it will be of no suprise that for this

particular system the bubble has a frequency at which it prefers to oscillate (the so-called natural

frequency). All other modes of oscillation will quickly decay leaving the natural mode to resonate the

longest (although it too will decay due to viscocity). This natural frequency is governed by the radius

of the bubble, the steady state pressure of the fluid as well as the ratio of specific heat of the gas

within the bubble and the density of the fluid. The equation for the natural frequency of a bubble is

given in the following expression {7}:

where:

gamma is the ratio of specific heat of the fluid

P sub zero is the steady state pressure

R sub zero is the steady state radius

rho is the density of the fluid

*{image borrowed from: water-energy.lbl.gov/ }*

One can witness firsthand the resonant frequency of bubbles simply by going for a swim in a lake

while it's raining outside (though if you live in a region with periodic lightning I would advise against

this). It turns out that when a water droplet (raindrop) impacts the surface of the lake, it sends an

oscillating bubble underneath the lake surface. Now this bubble oscillates mostly at it's natural

resonant frequency. Raindrops, being approximatly the same size produce approximately the same

size bubbles and consequently a relatively narrow range of sound frequencies is produced. Thus the

sound you hear underwater during rain results not from the actual impact of the water droplets upon

the lake's surface, but rather from the resonant frequencies of the generated bubbles (see photo

sequence below){7}.

{image borrowed, and modified from: http://www.physicstoday.org/pt/vol-56/iss-2/captions/p36cap1.html }

You can see in the above sequence that a tiny bubble is produced at impact, this tiny bubble (as seen

in the last few photos) is wholly responsible for the audible sound produced under the water. This

interesting phenomena is not nearly so strange as some of the other "bubbles" known to exist.