It's bonfire weekend here in the UK, and everybody is intent on shooting fireworks.
I was wondering, what determines the pitch of the sound produced by an explosion?
The sound has clearly a dominant mid-range pitch, around a few hundred hertz, and bigger fireworks also have a very low, but large component at around 20-50 hertz.
What determines this pitch? The amount of explosive energy? The shape of the vessel? Something else?
Best Answer
I will go mostly with Chad's argumentation. Larger equals slower, which should excite relatively more low frequency sound. Also note that the larger the blast (hopefully) the further away the observer is. And air is not a perfectly elastic acoustic medium, some energy is lost, and the higher frequencies attenuate quicker than shorter, so distance will selectively filter out the higher frequencies.
Also, note, explosion usually means detonation. A detonation is an exothermic reaction which spreads by the compression (adiabatic) heating from the shockwave, and the chemical energy maintains the shockwave. A shockwave is essentially a highly nonlinear soundwave, and as the overpressure decays with distance from the source is will grade into a soundwave. Fireworks (pyrotechnics) are not explosives, but are the (relatively) slow reaction of chemicals (combustables, and an oxidizer) due to heat. Fireworks may generate shockwaves in air, if the package ruptures at sufficiently high pressure. Likewise volcanic blasts are not detonations, but shockwaves formed by the escape of high pressure gas.
If an explosion is fast compared to the sound frequencies the detector is sensitive to (probably human ears in your case), then we might be able to model the explosion as a delta-function in time. A delta function should equally excite all frequencies, so it should be a simple matter of distance attenuation of sound waves.
An explosion close to a solid surface, creates an amazing effect I've heard called a mach-stem (although wikipedia does not produce anything useful for this term). In any case, at fixed distance the near surface shock wave is much stronger than the shockwave at height above ground. In essence the ground effect part of the shockwave weakens roughly only as 1/R rather that the 1/R**2 one would expect for a free air spherical blastwave. I don't know what effect this has on the sound spectrum (pitch), but you need to be at a much larger standoff distance from a near groundblast than from a samesized high altitude blast because of it.