So I am trying to create a RTSP server that streams music.
I do not understand how the server plays a music and different requests get what ever is playing at that time.
You should first be clear about what is RTSP and RTP. The Real Time Streaming Protocol (RTSP) is a network control protocol designed for use in communications systems to control streaming media servers. where as Most RTSP servers use the Real-time Transport Protocol (RTP) for media stream delivery. RTP uses UDP to deliver the Packet Stream. try to Understanding these concepts.
then Have a look at this project. http://sourceforge.net/projects/unvedu/
This a open source project developed by our university, which is used to stream video(MKV) and audio file over UDP.