Since a sonic boom is just a collection of pressure waves combined into one massive pressure wave, would the low pressure zone behind it be enough to put out a large fire?
[Physics] Can a sonic boom put out a fire
acousticspressureshock-waves
Related Solutions
Sure.
It would happen all the time with propellers and rotors if we didn't design them to avoid it.
This is something that is generally avoided in aerospace applications because the shock wave causes pretty significant drag. A lot of work goes into making sure this doesn't happen through careful selection of the blade cross section, adding sweep the blades, and changing the design so the radius is smaller and the velocities therefore lower.
Shock waves will only form when the normal velocity exceeds the speed of sound. So sweeping the blade changes the angle the leading edge makes with the air and therefore lowers the normal Mach number. This prevents shocks from forming until higher velocities are reached. Odds are very good that the fan inside your Dyson has blades that are swept at the tips to prevent really loud and annoying noise generation.
This gives us designs that look like (source):
Background
The way to reduce the sound is to reduce the pressure change across the shock, which can be done using an oblique shock.
In this case, the angle between the shock surface and the incident flow speed, $\beta$, enters into the pressure ratio for a hydrodynamic shock as: $$ \frac{P_{2}}{P_{1}} = 1 + \frac{ 2 \ \gamma }{ \gamma + 1 } \left( M_{1}^{2} \ \sin^{2} \beta - 1 \right) \tag{1} $$ where the subscripts $1$ and $2$ correspond to the upstream and downstream regions, respectively, $\gamma$ is the ratio of specific heats, $M_{j}$ is the Mach number in the $j$ region, and $P_{j}$ is the average pressure in the $j$ region.
As you can see, in the limit as $\beta \rightarrow 90^{\circ}$, we approach the standard expected limit for a hydrodynamic shock. This is equivalent to looking at a shock produced by a piston/driver with a planar surface orthogonal to the incident flow.
The magnitude of the pressure ratio, or the overpressure, defines the strength of the sound wave of the sonic boom at the source. If we measure this in decibels, then we can see from the description at https://physics.stackexchange.com/a/266046/59023 that the intensity observed goes as: $$ L_{r}\left( r \right) = L_{i,src} + 20 \ \log_{10} \left( \frac{ 1 }{ r } \right) \tag{2} $$ where $L_{i,src}$ is the intensity level at the source and $r$ is the distance from the source. This is one of the reasons why one solution proposed is to fly a supersonic jet at higher altitudes (other reasons are outlined in the above linked answer relating to sound attenuation at altitude).
Answers
Is it still a wave?
Well, that's a little trick since a sonic boom is what your ear registers when a supersonic object passes by. It is the result of a shock wave, which is inappropriately named as I discussed at https://physics.stackexchange.com/a/136596/59023.
Furthermore, if it is a wave, why does it make a boom sound and does it have a decibel number?
The boom is a discontinuous pressure pulse (well, technically it's two, an over- and underpressure pulse). Yes, one can estimate the decibel level as I described above in Equation 2.
Can we measure the decibels?
Yes.
All of this leads me to the question, is it possible to counteract, or cancel, the noise of a sonic boom?
Cancel, probably not. Reduce greatly, probably yes. One way is to change the shape of the nose cone of the jet, which alters the shock geometry (as I discussed above). For certain geometries, one can get a reduced pressure ratio (e.g., Equation 1) and thus, a smaller overpressure sound wave resulting in a "quieter" sonic boom.
Reference
The phase diagram image was taken from Wikipedia, courtesy of EMBaero - Own work, CC BY-SA 3.0, https://en.wikipedia.org/wiki/File:Obliqueshock.PNG
Best Answer
Acoustic suppression of flame is viable. It can happen in one of two ways:
(1) Continuous sound waves may interact with flames and accelerate air and vaporized fuel particles, which drops the temperature of the flame and disrupts the flame boundary layer between the hot gas flame and the vaporized fuel. When flames are extinguished, vaporized fuel ceases to burn. However, if un-vaporized fuel remains hot enough, it will flare up again when the sound waves cease.
(2) A shock wave, or blast wave, may displace hot gas and vaporized fuel from the source of a fire, and spread it over a wide area, cooling it and extinguishing the flame. This method is used with oil and gas wellhead fires. If un-vaporized fuel at the wellhead remains below combustion temperature, this allows time for firefighters to stop the flow of fuel.
It's not so much the low pressure zone behind a shock wave, as it is the displacement effect of the wave front that extinguishes flame by accelerating and dispersing vaporized fuel (either from liquids or from burning solids) and hot gas, separating fuel vapor from the hot gas of the flame.
If the energy in a sonic boom emanating from an aircraft high in the atmosphere were great enough, it could disperse flames. But I doubt such energy could be achieved unless the wavefront were concentrated into a small area. Pressure at ground level caused by sonic booms generally is under two pounds per square foot.
Alternatively, a shock wave emanating from a powerful explosion (nuclear, dynamite, etc.) can extinguish flames. But if unvaporized fuel remains at combustion temperature, it will flare up again.