Abstract:
The Doppler effect is a well-known and widely used phenomenon. In acoustics it is usually considered for linear response from a moving target. No attention was given previously to specific phenomena of nonlinear sound scattering by moving nonlinear scatterers. In the present paper a nonlinear analog of the Doppler effect is studied theoretically and experimentally. The most prominent nonlinear acoustic scatterer is a bubble. A theoretical analysis of frequency shift under nonlinear scattering of two, in a general case, acoustic waves by a moving nonlinear scatterer with generation of harmonics and combination (i.e., the sum and the difference) frequencies is given. It is shown that the nonlinear Doppler frequency shift for the difference frequency generation depends on the geometry of primary waves and can be much larger than the linear Doppler frequency shift for the difference frequency. Experiments have been made with bubble flows in a vessel. The results are in good agreement with the theory. Feasible applications of the nonlinear Doppler effect for bubble flow velocity measurement are discussed and demonstrated experimentally. [This work was done at the Acoustic Research Lab. of Sung Kyun Kwan Univ. under support of STEPI, Republic of Korea, and supported in part by RFBR (grant 94-05-16755), Russia.]