[NOT THE BLUE LAMPSHADE]

a clapping noise? if it is your calipers or some goofy shit being loose, then its your warped rotors just intensifying the noise, all sorts of weird noises happen on different cars when your rotors are warped because initial application of the brakes shakes things up quite a bit, but that would be at higher speeds (what is low speeds to you 15-30 or like semi-hwy 40-50ish)
i had a caliper bolt brake off on my talon and it was really bad braking below 30 or 40 but not too terrible on the hwy, i pooped a little when i figured out what happened

It may not even be a brake problem, besides the warped rotors obviously, the shaking may be causing something else to be wobbling around or whatever like a shitty ball joint, tie rod, i dunno, whatever else

have you checked your pads through the top of the caliper? how much is left? Maybe you do have a cracked rotor or you could be missing one of the plates or something hilarious, ive fixed 3 cars this winter with the inside rotor plate missing, just the vents goin to town on the caliper piston