The Doppler frequency of reflected light from a moving mirror is measured using a Michelson interferometer and a low cost spectrum analyzer. The experimental data for the Doppler frequency are in agreement with the calculated theoretical values with a standard percent error of 0.54%. The concept of optical mixing of a phase-modulated signal with the Doppler signal is presented, with a derivation of the resulting detected signal power, using the small phase modulation amplitude approximation. An experiment is described using laser Doppler velocimetry to heterodyne the Doppler signal with an acoustic wave. The experiment provides a good illustration of the Doppler effect, spectral analysis, and principles of optical mixing and interferometry in an advanced undergraduate laboratory.