Direct measurements of the spectral purity in terahertz femtosecond-demodulation sources are reported and compared to theory. Because these sources operate at very high harmonics (∼102 - 104) of the mode-lock frequency, a high spectral purity source is very dependent on a low-jitter femtosecond laser. Conversely, the spectral content of the terahertz sources provides detailed information about timing jitter and stringent tests of models used to describe the jitter. We find that both the behavior of the central core, and the noise skirts of the power spectrum of our sources, can be quantitatively related to measured ripple and continuum amplitude noise on the Ar+ pump laser by use of modulation theory.