The design and application of a frequency sweep (FS) interferometer for sound speed measurements on high-temperature silicate liquids, with the potential to be applied to liquids at high pressure, are presented. FS interferometry differs from variable path length interferometry in that no mechanical movement of a buffer rod is required. Instead, a wideband pulse spanning 1--2 MHz is transmitted down the upper buffer rod, which allows maxima/minima in the returned signal to be evaluated as a periodic function of frequency. Measurements may be made at several different centered frequencies (from 3 to 7 MHz with the transducer used in this apparatus) in order to test whether the liquid sound speed is frequency-independent and thus relaxed. This paper describes the mechanical assembly and the algorithms for signal and data processing, which are based on the solutions to the wave equations in a rod-liquid-rod interferometer. The precision and accuracy of the FS interferometer is demonstrated by measuring the relaxed sound velocities in six liquids (NaCl, a sodium silicate, two sodium aluminosilicates, CaMgSi2O6, and Fe2SiO4) with well-known sound speeds from the literature.