Particles in an acoustic wave oscillate over time around a certain position with a certain amplitude. The velocity v expresses the velocity of the particle over time. It is related to the pressure by the impedance of the medium : v = p/real(Z) = sqrt(cw/real(Z)), where c is the speed of sound and w the frequency.

I simply wanted to ask about the equation: lambda*F=Va ,  where lambda is the distance between grating  maxima  ( the grating here refers to the modulation of the refractive index which the acoustic wave creates in the medium) , F is the frequency of the acoustic wave, and Va is the velocity of the acoustic wave in the medium. If we change the acoustic wave frequency F does the lambda change so that the acoustic velocity in the medium Va remains constant? 

dear vladimir

If you are speaking of the wave celerity dispersion in material, I can say yes it occurs. It can depend on the kind of waves (see lamb waves for example) or on the material heterogeneity.

If your medium is liquid or solid, I believe there will be dispersion (celerity changes with the frequency of the wave).

The dependence of acoustic wave velocity on frequency itself depends on the medium.  For water, which is one of the most common applications for acoustic propagation, the sound velocity is usually considered independent of frequency over the range of practical applications (a few Hz to MHz).  In solids, such as in the sea bed, this is no longer the case, and of course one has to consider both compressional and shear waves in solids.

The frequency dependency of velocity for the various waves which can propagate in a medium depends on:

a) the nature of the medium: gas or liquid

b) isotropic / anisotropic

c) homogeneous / nonhomogeneous

d) bounded (guided modes) / unbounded

I suggest the reference:

Ultrasonic Methods in Solid State Physics

By Rohn Truell, Charles Elbaum, Bruce B. Chick; Academic Press, 1969.

I hope this will help ...