Acoustical Doppler effect analysis-Is it a valid method?

The Doppler effect approach is a powerful tool used in various areas of physics to analyze motion in a wave field, by observing the frequency shifts of scattered waves. In acoustics, Doppler effect analysis is used for diagnostics in biomedical systems and for industrial applications, e.g., in cases where scatterers are present in moving fluids. The theoretical models used to analyze such systems usually ignore the fact that the moving ambient medium might produce effects of the same order of magnitude as the scatterers themselves. It has even been argued that in certain circumstances such effects should completely cancel the Doppler frequency shifts. A model is developed here that contributes to our understanding of the scattering in the presence of moving objects and space- and time-dependent moving media. The model is restricted to irrotational flows, neglects velocity effects except of the first order in the Mach number v/c, and assumes slow variations in the ambient medium. These restrictions facilitate the analytical discussion of specific canonical problems. The present study indicates that Doppler effects can be produced by moving scatterers in a medium at rest, scatterers at rest in a moving medium, and in configurations in which combined motion of scatterers and media take place. The Doppler effects are of the same order of magnitude in all cases. This vindicates the simple models used for research and applications, which assume that the moving objects produce Doppler effects but neglect the flow of the surrounding medium. PACS numbers: 43.20.Bi, 43.20.Fn.