A good ear for clean acoustics and sound is required of a Sound Designer. A physics or electrical/electronics engineering background would be really beneficial.
In Pune, there is a Sound Designing course offered by FTII. In Chennai, there is also the School of Audio Engineering, which is a fantastic sound school. For further music-related alternatives, go into KM Music Conservatory (AR Rahman’s Music School).
Please keep in mind, however, that a career in sound design and recording is quite difficult and needs a lot of ingenuity. It’s not the same as getting into an institute and receiving a break. You must have a natural ear for music.