Is there a "Planck's constant" equivalent for phonons, sound particles As per de Broglie's Law, every wave has a particle nature associated with it. I tried to find what sound particles are called, and I got that they are phonons.
Now, I am curious about what it's energy will be. We have for light:
$$E_{\text{photon}}=h\nu$$
I suspect a similar energy equation for phonons must exist.
$$E_{\text{phonon}}=k\nu$$
where $k$ is a proportionality constant.
What could this $k$ be?
 A: Sound waves are typically made up of a large amount of phonons. 
The energy of a phonon is E = hf where h is planks constant and f is the frequency of the wave whether transverse or longitudinal. 
Let me know if you need any clarifications.
A: You just use the same Planck constant.
Photons are the quantized excitations of the electromagnetic field. Phonons (which generally only occur in solids) are excitations of the displacement field of the nuclei. As such, they're really not very different at all, and they're treated in exactly the same way by quantum mechanics, including of course the basic identification of frequency with energy - otherwise just known as the Schrödinger equation,
$$
i\hbar \frac{\partial}{\partial t}\psi = H\psi,
$$
where $i\frac{\partial }{\partial t}$ measures the temporal frequency of the wavefunction $\psi$, and $H$ is known as the hamiltonian and gives the energy of the system. This equation is universal to quantum mechanics, and the constant that links the two is always the same Planck constant $\hbar$.
