The Pocket Rocket (Concorde) leaves a horizontal cone-shaped sonic boom behind it (with Concorde at the apex). This is spreading out at the speed of sound (in a pressure front). It will spread down and reach the ground in a hyperbolic shape (viewed from above) that is moving at the same speed as the supersonic aeroplane. Any point on the ground in the carpet of the sound will hear a double boom as the pressure wave passes caused by the leading edge and trailing edge of the machine.
Is it something to get excited about? Supersonic ops are conducted away from populated areas to minimise nuisance, so it's not a problem, the peripheries of affected areas only receive a weak 'boom' (either end of that hyperbolic pressure wave moving over the ground). Ever stood on a pavement and heard a loud lorry moving past? Had one of those awful Jap motorbikes with a 'tweaked' exhaust accelerate past you? Worked with noisy machinery, or been troubled by it? Had trash pickups at 4 am? (favourite Australian trick). There are far more important sources of sound pollution, but Concorde always made a glamorous target for complaints!