We calculate the unusual Doppler effect in the B phase of superfluid He-3 i
n the Ginzburg-Landau regime and at low temperatures. We analyze the nontri
vial dependence of the sound velocities and of the internal Doppler-shift c
oefficients on the superfluid velocity in the Ginzburg-Landau regime. The v
alue of the fourth-sound Doppler-shift coefficient is most remarkable: it e
xceeds 2.2 (the intuitive order of magnitude is 1). [S0031-9007(98)07981-2]
.