The answer to 'why is my sink burst pipe' is that a burst pipe under the sink is usually caused by a frozen or clogged pipe that has built up too much pressure. Common symptoms include a leak, water pooling, or the pipe bursting completely. Solutions may involve thawing the pipe, unclogging the drain, or replacing the damaged section of pipe.
If the burst pipe is localized under the sink, it may be possible to DIY the repair by shutting off the water supply, disassembling the sink, and replacing the damaged pipe. However, if the issue is more widespread or the pipe is difficult to access, it's best to call a professional plumber who can properly diagnose and fix the problem.