why 48Khz for video and 44.1khz for music?

music has always traditionally been at 44.1

The CD standard is 44.1 kHz.   But you'll find a lot of digital files (music for download) at 48 kHz and higher.

In the early days of digital audio the music was edited and mastered on modified video recorders, 44.1k was chosen because an exact number of audio samples would work with both PAL and NTSC recorders. With the D to A converters at that time the sample frequency was regarded as a bit low so when video production moved to digital audio using DAT tapes and digibeta 48k was used to get better quality. With modern oversampling D to As the difference is now negligible. 

We use 48 kHz for audio embedded with the video because the audio processors that are used in consumer electronics devices such as DVD players and PC soundcards have native steps that are multiples of 48 kHz (this is due to the nature of CPU clock technology). Using 44.1 kHz for the audio would require resampling to a multiple of 48 kHz in either hardware or software. Unfortunately, the resampling alogarithms in some devices can - and do - cause unwanted artifacts, some of which are noticeable and audible.