First, yes the speed of sound is the limit of the group velocity at small wave vectors. In the limit of small wave vectors (long wavelengths), the material acts like the continuum material we see at a macroscopic scale. (You don't see any atoms with your eye. Macroscopic materials appear to be infinitely divisible.) The speed of these long-wavelength waves is "the speed of sound".
However, be aware that there is not simply a single speed of sound in solids. Solids support many types of waves (longitudinal, transverse, Rayleigh, etc.), and each has its own "speed of sound". In contrast, there is only one type of wave in air (a pressure wave) so there is only one speed of sound. Things can be even more complicated still because materials can be anisotropic; the wave speed is different in different directions.
Now that all that is said, let's examine your question. All you specify is a frequency. You also need to specify a mode and a direction. A 1 MHz transverse wave will have a different speed (and thus a different wavelength) than a 1 MHz longitudinal wave. Likewise, what direction is the wave propagating in? This makes things complicated since the group velocity and the wave vector can be in different directions for an anisotropic material.
In short, you haven't given enough information about your system.
You'd have to provide information like: a sound wave in air could hit an isotropic solid normal to its surface. Then I could say that the pressure wave in air will excite a longitudinal wave in the solid, and we could go from there.
Also, as @garyp notes, the intensity of the sound has absolutely nothing to do with finding a point on a dispersion relation.