This paper describes a fiber-optic spectrometer for measuring the wavelength of light sources. This device makes use of an acousto-optic modulator to frequency shift counter-propagating light beams in a Sagnac fiber-optic interferometer. The fringe spacing at the output is a function of the wavelength of the light source and the frequency difference of the two counterpropagating light beams. This same device was used to determine the length of the fiber coil ofothe spectrometer. Experiments showed that the resolution of the spectrometer was 0.007 Å and the optical pathlength resolution was 8 microns. Applications of this device include the characterization of optical fibers and light sources under dynamic conditions.