Loose kitchen sink waste water pipe has come loose

overflow from sink.

is the black flexi pipe roughly 1 inch wide if so its the overflow pipe so it has either come off from the top of the sink behind the either rectangular or round overflow and needs putting back on if not it will have come out of the bottom of the waste in the sink or may have even split its hard to guess without seeing but if you can look under sink or even take a picture i could help you further some only push back on over a collar and better quality ones will have a nut and washer attached to waste

The over flow pipe from the sink

It sounds like a flexi waste from your p trap, it may have just need the nuts tightening onto the trap properly

This is the overflow pipe. It is connected at one end to the combi-waste attached to the drain hole in the sink, and at the other to a fitment at the back of the sink ( the overflow ). Ensure both ends are connected. Usually both are push fit. If either end is a loose fit, buy a new combi-waste kit. They cost less than £5.