An acousto-optic modulator sends an acoustic (sound) wave with frequency $\nu_s$ through a crystal, forming a moving diffraction grating something like the illustration you provided. Sending a laser beam with frequency $\nu_l$ through the grating results in multiple diffraction orders, with shifted frequency $\nu_l +n\nu_s$, where n is the diffraction order number.
So yes, it's possible to shift the frequency of light using sound.
However, acoustic frequencies, even in an acousto-optic modulator, are much lower than laser frequencies. Green light at 540 nm has a frequency of about 560 x $10^{12}$ Hz, while the fastest A-O modulator use an acoustic frequency of about 1 x $10^9$ Hz. That means an A-O modulator can change the frequency of green light by at most a few parts in 560,000. The human eye can distinguish light frequency differences as color differences, at best on the order of 2 parts in 500. So, an A-O modulator would need to use an acoustic frequency about 1000 time higher than is currently possible, in order to shift visible light frequencies enough to be perceived by human vision. It would be hard to call such a high frequency "acoustic"!