The acoustic phonons are related to the propagation of sound. If you can find speed of sounds measurements, e.g., look into Brillouin light scattering, you get an estimate  for the acoustic frequencies according omega=k speed of sound. You can also also calculate the speed of sound from bulk modulus and mass density. 

Thanks Christian for  your answer.

I still want to ask you, if I know the value of speed of sound, which K (wave vector) value should I use? sorry I am no expert in this area. Also I´ve found some data on frequency shifts from Brillouin light scattering, is this  equivalent to phonon frequency? how do I get the frequency of the absorved phonon? I appreciate your help cheers..

The relation Omega=k*speed of sound is actually nothing but the almost trivial relation frequency*wavelength=speed of wave propagation. There is not one acoustic frequency but an entire branch which starts at k=0 (meaning infinite wavelength) and ends at the maximum k vector of the first  Brillouin zone (in one dimension k=Pi/a). The maximum wavelength corresponds to maximum use of the "springs" between the atoms when they vibrate fully antiphase. In other words for every wavelength there is a frequency . The product is the constant sped of sound in the regime of linear dispersion near k=0.Physical quantities, such as the heat capacity, depend on the integral over all wavelengths. Brilluoin light scattering can measure excitation with wave-vector near k=0. This often are the phonons (quantized acoustic waves), but can also be magnons for instance. You need to check what they measured. 

Thanks Christian we did the following, please give me your opinion:

"we use the measurement of speed of sound in amorphous Al2O3 obtained using picosecond ultrasonic technique by Rossignol et. al.( PRB 70,094102) Here speed of sound yields the longitudinal sound velocity v_Al2O3 = 6.7 x 103 m/s.

Considering a value of k=Pi/2a at the middle of the first Brillouin zone, from the expression ω = v_Al2O3 * k; a value of phonon frequency ω = 2.24 x 1013 sec-1 is obtained."

If you agree I would like to send you via email somehow  longer text on the paper we are writting  as your opinion is very valuable.  Cheers 

If you want to ignore the fact that there is dispersion and somehow express everything in an effective frequency your approach seems like a meaningful approximation. Whether that in fact makes sense depends on the problem you want to consider. For example, in the theory of heat capacity of solids there is indeed the so called Einstein model which ignores dispersion and assumes that every mode has the same frequency called the Einstein frequency.

 The meaning of acoustic branch in a dispersion relation is to be seen in contrast to optical phonons which appear in solids with more than one atom per unit cell. Those modes have a dipole moment and thus can be excited by the E-field of a light wave (hence the name optical). They are higher in energy and in particular there is a non-zero frequency associated with infinite phonon wavelength. LIght scattering experiments such as Raman or infra-red scattering measure those k=0 optical phonons (because a light wave has see little momentum in comparison to phonons near the Brillouin zone boundary). 

Optical and acoustic phonon branches coexist. There are always acoustic phonons and there can be optical phonons. In Al2O3 thre ar both. The acoustic phonons are those related to sound propagation. In all cases phonons refer to motion of atoms around their equilibrium positions.  

Thanks to both for the interesting disscussion. I am acctually intested in the "average" acoustical phonon frequency. This is why I take the value of K at the middle of the first Brillouin zone. What is your opinion of this appoach? I want to compare this value with other experiment where I manage to extract average phonon frequency.  

Second question in case you know the answer, since I am not familiar with the traditional experimental techniques to meassure phonon frequency (e.g. speed of sound meassurements), I would like to ask you how difficult is to meassure this ? I have seen people meassure it in rather thick films. For ultra thin films about 2 nm I believe this is not an easy task however I am not sure of this. Any comments on this would be of great help. Cheers

sound velocity v= ( Ceff/p)^1/2

p=density

Ceff= elastic constant

example

TA sound velocity= (C44/p)^1/2, in the [100]

LA sound velocity=(C11/p)^1/2