The aim of this work is to understand the minimum physics that leads to density waves in a fluidized bed. Most previous models assume two inter-penetrating phases which leads to separate equations of motion for the fluid and solid phases. In this work, the two phase model has been simplified to a single phase one by assuming that the slip velocity between the solid and gas phases is a constant. In effect, the bed is modeled as a compressible fluid that is also acted upon by a density-dependent force. Continuation and bifurcation analysis are used in order to understand how the uniform solution loses stability and one dimensional traveling wave solutions are born. It is shown that the salient features of the instability of a gas-fluidized bed are captured by the basic physics of compressible flows.