When a small test wave is launched near the frequency of a large amplitude electron plasma wave, the behavior of the test wave is determined by the nonlinear dynamics of the electrons that are trapped by the large amplitude wave. Consequently, the amplitude of the test wave oscillates coherently with the trapping oscillations in the amplitude of the main wave. The behavior of a small, launched, test wave at frequency ω is observed as a function of its frequency separation from a large amplitude electron plasma wave at frequency ω0. The initial damping and subsequent amplitude oscillations of the test wave are compared with a calculation in which the test wave is treated as a slow modulation of the amplitude and phase of the main wave. Test wave experiments agree with the calculation when ω0 − 4π/T < ω < ω0 + π/T, where T is the transit time of the main wave through the experiment. When the spontaneously unstable frequency of the lower sideband is within this range, the slow amplitude oscillations of the sideband agree with the calculation. When the frequency of the test wave is sufficiently far below ω0 − 4π/T, the test wave damps according to linear theory. The phase velocity at which the test wave behaves essentially linearly determines the velocity of the fastest electrons that interact strongly with the wave.