Redshift of acoustic waves in acoustic streaming

Redshift, namely, the frequency decline in the frequency spectrum of an acoustic wave in water, was observed by measuring the frequency spectrum of acoustic streaming in a standing wave field. We desire that relations of the energy ɛ and momentum μ of acoustic waves analogous to those under quantum conditions hold, that is, $\varepsilon {=n}_pħ\omega ,$ $\mu {=n}_pħk,$ where $ħ=h/2\mathrm{}\pi$ (h is Planck’s constant), $n_p$ is the phonon density, ω is the angular frequency, and k is the wave number. In this case, a redshift indicates that acoustic waves suffer energy loss or annihilation of phonons. We show that the driving force of streaming is derived from the momentum transfer of phonons and the direct conversion of energy from acoustic energy to kinetic energy of the medium.