Methods and systems are provided for monitoring a solid-liquid interface, including providing a vessel configured to contain an at least partially melted material; detecting radiation reflected from a surface of a liquid portion of the at least partially melted material; providing sound energy to the surface; measuring a disturbance on the surface; calculating at least one frequency associated with the disturbance; and determining a thickness of the liquid portion based on the at least one frequency, wherein the thickness is calculated based on L=(2m−1)vs/4f, where f is the frequency where the disturbance has an amplitude maximum, vs is the speed of sound in the material, and m is a positive integer (1, 2, 3, . . . ).