The phase and amplitude spectra of the S waves radiated from five different bilateral, tensile fractures in two-dimensional models are discussed. Two S waves, radiated in approximately opposite directions, were recorded for each fracture. The amplitude spectra display the regular sequence of holes first explained by Ben-Menahem. The phase spectra display a phase jump of π radians associated with each hole in the corresponding amplitude spectrum. The phase of the source-time function was extracted from the phase spectra; it is consistent with a representation of the source-time function by a ramp function of 14 μsec duration. An explanation of the observed spectra is given in terms of interference between the initial and stopping phases of the radiated signal. From this viewpoint Ben-Menahem's directivity method is seen as a procedure for detecting the stopping phase in dispersed wave trains. Finally, it is suggested that the analyses by Ben-Menahem and Toksöz of the phase spectra of the Kamchatka 1952 and Alaska 1958 earthquakes have not properly taken account of the phase jumps in the spectra.