Well, you are correct about different ways to mitigate the booms, but that wasn't much of a priority in the Shuttle, I'd guess. any object or part of one that is moving faster than the local
speed
of
sound will create a 'boom/noise.' That could be the tip of a whip, the tip of a propeller, even parts of an airliner, although usually not in normal operations. Of course, if the whole object is moving faster than the SOS, everything in the airstream
could be creating a sonic-boom/noise. But unless you were extremely close and had super-human ears, it would sound like a single 'boom.' And the farther away you are the more 'thunderous' it would sound as the higher freqs fade faster than the longer waves. The reason for a double boom, no matter what creates it is the shear power and magnitude or the wave. Remember, air is compressible. When the shock wave passes through the air, it actually compresses the air which then rebounds back to its normal atmospheric pressure. But with a massive, very strong wave, the air compresses so much that the rebound actually lowers its pressure much below the normal pressure! Now, when that 'decompressed' air 'realizes' its condition, it immediately tries to
repressurize itself, and makes a smaller but closely following, secondary 'boom.' The original is still a single, combined wave made up of any and all the mini-shocks caused by the object, they just end up munged together and 'confused.' But they are so powerful they cause the secondary shock wave.
That's my story, anyway!