In the recent years, we have shown that cylindrical biological membranes such as nerve axons under physiological conditions are able to support stable electromechanical pulses called solitons. These pulses share many similarities with the nervous impulse, for example, the propagationvelocity aswell as themeasuredreversibleheat productionandchanges in thickness and length that cannot be explained with traditional nerve models. A necessary condition for solitary pulse propagation is the simultaneous existence of nonlinearity and dispersion, that is, the dependence of the speed of sound on density and frequency. A prerequisite for the nonlinearity is the presence of a chain-melting transition close to physiological temperatures. The transition causes a density dependence of the elastic constants which can easily be determined by an experiment. The frequency dependence is more difficult to determine. The typical timescale of a nerve pulse is 1 ms, corresponding to a characteristic frequency in the range up to 1 kHz. Dispersion in the sub-kilohertz regime is difficult to measure due to the very long wave lengths involved. In this contribution, we address theoretically the dispersion of the speed of sound in lipid membranes and relate it to experimentally accessible relaxation times by using linear response theory. This ultimately leads to an extension of the differential equation for soliton propagation.