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It is an accepted fact that transverse Doppler effects of the first order in v/c are nonexistent for all physical wave phenomena, including acoustics, i.e., the Doppler effect is zero for radiation normal to the direction of motion. However, this statement assumes that the incident field is a plane wave, which is not true in general for finite aperture sources. Consequently, the probing of flows transverse to the axis of finite diameter beams, particularly focused beams, is feasible. This geometry will be advantageous in many applications where the classical orientation of the sound beam, oblique to the flow, is not possible. With this motivation in mind, the theory and experimental feasibility of measuring Doppler spectra in transverse geometries is presently investigated.