To measure the velocity of the smallest particles suspended in the flowing fluid, an interference pattern is used, as shown in the figure.

A parallel beam of light from a laser with $\lambda = 630$ nm is incident on two identical prisms stacked on their bases (bi-prism). The refractive angle of each of the prisms is $\alpha = 5,7$ degrees and the refractive index is $n = 1.5$ After passing through the bi-prism, the light splits into two beams that pass through the cuvette with liquid. The particles, moving together with the liquid with some velocity v, scatter the light.

Determine the velocity of the particles if it is known that when the photo-detector registers the scattered light, the frequency of the photo-detector current fluctuations is $f = 10$ kHz.