Never operated L1011s but I know what you mean from years of hanging around ramps as a despatcher and pilot!
The start process is the same as just about any other turbine engine; the core section is spun to a certain RPM, the fuel is introduced, then ignited. The "Boom" you speak of is simply the fuel suddenly burning. The same process can be heard on any other engine if you're in the right place.
Large fans like RB-211 have correspondingly heavy rotating machinery, which takes more time to spin up than, say, a tiny 146 engine, which is why it takes so long and keeps you in suspense.
Some turbines are started by electric starter motors, some by forcing compressed air through the engine from the APU or an external Air Start cart. If its air started, the hissing of the escaping air often masks the sound of ignition.
Anyone know whether the RB-211 is air or electric start?
The characteristic start behavior of the L1011's RB-211s is therefore due to the exact timing of fuel on, followed by ignition, which results in more fuel being in the back of the engine than the ignitors can immediately deal with, bearing in mind the slow rotation at that time. Interesting that RR powered 747s don't make the same sound. Or put out the same smoke.
The sound must be simply the acoustics of the cowling and the hot section exhaust design.
But I repeat, I've no history with the type or its engine, just thought I'd offer the above until an RB-211 mechanic provides the expert answer!
Others with interesting start noise are BAC-111s and Tu-154s!
Regards - Musang