The effects of time-dependent electron density fluctuations on a synthesized time domain reflectometry response of a one-dimensional cold plasma sheath are considered. Numerical solutions of the Helmholtz wave equation, which describes the electric field of a normally incident plane wave in a specified static electron density profile, are used. Included in this work is a study of the effects of Doppler shifts resulting from moving density fluctuations in the electron density profile of the sheath.