Short Answer – No research to date supports this (but it probably won’t hurt your baby).

A fetus’ ability to hear is developed by the second trimester, so they can hear music… but no one is really sure if listening to Mozart is soothing and satisfying, or just annoying to a developing child.

If you decide to try it, keep in mind that amniotic fluid is a good conductor of sound, so you don’t need to turn the volume up very high for your baby to hear. Putting headphones on your belly isn’t needed, and it might, in fact, scare or over stimulate your baby.  

If you want to play music for your little one, play it in the background like you would for yourself and keep it to 50 decibels or lower.