Popping “vacuum bubbles” loudness

Stun-wizards specialize in blinding and deafening opponents at a distance. To do so, they can exert their magical power to manifest a spherical region of vacuum by essentially "telekinetically" pushing air out of the region. When the wizard releases their spell, air rushes back into the space, presumably with a loud "bang".

How do you calculate the acoustic loudness (in sound pressure, dB) of a sphere of vacuum, with arbitrary radius r, collapsing at a regular atmospheric pressure?

• magic and hard-science? – L.Dutch - Reinstate Monica Jan 23 at 14:56
• @L.Dutch-ReinstateMonica Eh, what I'm looking for is the concrete mathematical calculation of an effect (which just happens to be caused by magic). How the vacuum bubble is created in the first place isn't what I'm asking for – Dragongeek Jan 23 at 15:01
• check out this video you will be disappointed! – user6760 Jan 23 at 15:05
• @user6760 It's hard to judge volume of something in a video due to automatic gain adjustment but it's still neat! – Dragongeek Jan 23 at 16:11
• @L.Dutch-ReinstateMonica It's a perfectly legitimate area of physics, it's just the background condition generating it that's magic. – BLT-Bub Jan 23 at 18:27

The collapse of bubbles on various scales has actually been an area of research for quite some time. Analyses are typically numerical, and rely on something known as the Rayleigh-Plesset equation, which tells you how the bubble's radius varies as it oscillates or collapses. If you know the pressure inside the bubble and the pressure far from the bubble, you can adequately predict its collapse by numerically solving the differential equation - you're not going to get an analytic solution in the general case.

Sound waves emitted by oscillating and collapsing bubbles - due to external perturbations - are discussed in Section 7 of Lauterborn & Kurz (2010). One of the earliest papers on solving the requisite equations is Hickling & Plesset (1964), which discusses the case of a bubble collapsing (and rebounding) in water. You may find that to be a good starting point. Regrettably, you'll have to carry out the numerical simulations on your own.

Some notes:

• The study of bubbles typically involves bubbles on the centimeter to nanometer scale; beware of assumptions that may become invalid at macroscopic scales.
• Solving the equations should give you the pressure of the shock waves; from there, you'll have to convert to decibels given the pressure of the external medium.
• This is a problem for which there is, unfortunately, no simple (i.e. analytic) solution.

Considering:

a) A small void-bubble would be relatively harmless

b) A medium sized bubble (enough to surround a person) would be by itself extremely useful in combat, taking away air to breath. The sound effects of it (if any) are secondary.

c) Sound is produced as air molecules move and collide against other molecules, or objects. To produce any sound that is louder than, say, a strong wind, you need a sonic boom, of air molecules moving at sound speed, on 1 atmo of pressure. We are talking of a really, really big bubble, city sized. If a mage can take away the air of an entire city, sound is irrelevant.

Much easier to stun someone by removing the air from around them for a few seconds.

Pops from collapsing vacuum bubbles are likely to be just that - pops rather than bangs, as they are only driven by 1 atmosphere of pressure. More pressure = louder bang.