The oscillations for a phonon traveling in the positive x direction can be approximated by a plane wave, y = A cos(kx - ωt), where A is the amplitude, k = 2π/λ is the wave number, and ω = 2π/T is the angular frequency.
(a) What is the speed of this phonon, cs, in terms of ω and k?
(b) If the momentum and energy are given by p = hk and ε = hω, how are the momentum, energy, and wave speed interrelated?