A general derivation is given for the Doppler-shifted received frequency due to source and receiver motion of uniform velocity in a steady-state, refractive medium with spatial gradients in velocity and temperature. The results from three cases of this generalized equation are especially important. First is the wind tunnel case, in which a stationary noise source is tested; in-flow or out-of-flow measurements at a fixed receiver should show no Doppler frequency shift. Second is the outdoor flyover noise test case, where a source is moving in an atmosphere with wind and temperature gradients. The Doppler frequency effects measured at a stationary microphone are different from those of the zero-wind, isothermal case; actual flyover data support this theoretical result. Third, the generalized Doppler frequency shift equation shows different frequencies of sound received by moving air particles at different heights; these frequencies can be incorporated into an atmospheric absorption model with varying wind and temperature.