It sounds like something clicking open or closed (like two bits of metal hitting each other), could it be a valve activating, or a spring? Does it keep doing it if you leave it running for a while?. could it be something to do with the refrigerant having settled over the winter, I know fridges and freezers can make some really funny/disconcerting noises if they've not been run for a while and the refrigerant in them has settled in away from the condenser.
I'm guessing that's a split unit in which case AFAIK there isn't much to the room unit as it's basically a radiator and a fan with a thermostat to call the external unit to turn on and possibly a valve.
Is air moving from the cooling vent? just in case the fan unit isn't turning and what you're hearing is some sort of reset switch kicking in and then trying again after a few seconds.