Why does a sitar have a buzzy sound?

The sitar's distinctive buzzing sound is the result of some complex things: the parabolic curve of the bridge, or jawari, causes the string to vibrate not like a guitar, but similar to a bowed string instrument. This is called Helmholtz motion. Here is a slow motion video capturing the Helmholtz motion of a bowed violin string:

As the string is plucked, the Helmholtz motion travels back and forth along the length of the string, and when the Helmholtz corner crosses the curved surface of the bridge, it causes the departure point of the string to change on the bridge. In physics, this is called a moving-boundary problem, and is very complex to model. Because the departure point changes, certain upper harmonics and partials are reinforced, and others are diminished, modulating the timbre of the string. This is what gives the sitar its characteristic sound. Here is an animation we made to demonstrate Helmholtz motion affecting the departure point of the string along the jawari surface:

Someone skilled in jawari work is not merely a fine craftsman doing something intuitively; they are physicists solving a complex problem!