In fact the Doppler shift would be fine as it is. I know in theory it should be "overdriven" to infinity, but, this being a type of singularity in nature, I expect the math equations for regular doppler shift to simply go a bit berserk if you insert v=c in there (where c is speed of wave motion in medium). And, if you overdrive the signal over clipping point (to produce the "boom") you probably won't be able to distinct the pitch anyway.
There are other ridiculous effects - such as, when you go supersonic you should in theory be able to hear your own engine sound
in reverse from the time when you weren't supersonic and the sound waves propagated ahead of you and you're now catching up with them.
As for the effect itself, I once researched what needs to be done in post-processing to make the fly-by sound
like a sonic boom. Here's what I produced:
http://www.youtube.com/watch?v=qtDJUpgpL3Q&hd=1#t=5m30sWhat you have here is "relatively simple" amplitude modulations:
-during approach, amplitude of fly-by sound is ramped to near zero
-during approach, amplitude of fly-by sound is increased to over clipping level but then quickly ramped back to 1 (nominal value)
It relies on the original fly-by sound (although I think at this point I used Tiger's fly-by sounds); however I didn't do anything to the frequency of the jet sound, only amplification.
This is a simplistic effect. It lacks the rumbling thunder-like characteristics of a sonic boom, because those actually come from the shock reflecting echoes from distance - just like the real thunder. Distance softens explosions and makes them lose most of their high pitch. A thunderclap happening very near you is a loud, powerful crack, whereas distant thunder gains a low, long-lasting rumble. As evidenced by multiple videos on youtube and elsewhere, a sonic boom happening very near to you would sound much like this to recording equipment.
Now based on what has been said by people who are actually involved in coding with the sound engine, I understand that doing this kind of amplitude modulation and getting it to correspond at the actual, accurate passing time would probably be a difficult task and low priority to accomplish.
I can't do it myself, I don't have nearly enough free time nor do I have the requisite understanding of the code, how to modify it, or the programming language in question. I'm not
expecting you guys specifically to jump on it and fulfill my demands, that'd be childish and unappreciative of the work you've already done.
I'm posting this because if, at some point, someone with dedication, free time, and necessary skill set decides to appoint significant part of their life to improving sonic booms in IL-2 1946 modded game, I'm fairly confident this is probably the simplest way to get it at least somewhat right. This might not happen ever, or it might happen after a month. But as long as I'm an active member of the community I'll be available for physics related consulting on the matter, because I do care about physical verisimilitude a great deal.
Anto, I really do appreciate all the work everyone's been doing with the supersonic coding. I especially like the Prandtl–Glauert singularity - it behaves very much like what I see in videos of supersonic aircraft, and gives a good visual representation of crossing the sound barrier.