Interest in tropical waves and their interaction with convection has been rekindled in recent years by the discovery, using satellite infrared data to track high cloud, that such waves closely display the dispersive properties of linear, inviscid wave theory for an atmosphere with a resting basic state and equivalent depths between 10 and 100 m. While several current approaches focus on internal modes in the atmosphere, this is inconsistent with the absence of internal modes in the atmosphere which is characterized by a single isolated eigenmode and a continuous spectrum. It will be shown, using an equilibrium type approach to convection, that the observed properties of waves are consistent with a continuous spectrum. The approach assumes that the total convection is determined by mean evaporation, but that the convection is patterned by zero averaged perturbations to triggering energy following the recent approach of Mapes. The observed convection associated with the migrating semidiurnal tide is used to calibrate the timescale for the convective response to patterning. It is shown that this time scale leads to the observed phase lead of low level convergence in tropical waves vis a vis the convective heating. Finally, it is shown that this phase is sensitive to the equivalent depth which it is suggested is the basis for the selection of equivalent depth. Detailed simulations of observed waves are readily obtained.