Dispersion and beats Consider two waves f,(x, t)- Acos(k, x-ot) and f,(x, t)- Acos(k2x- co, t) that propagate through the same medium. Assume ΔΚ-ki-k2 is much smaller than ki and k2. we saw in Lecture 6 that the resulting wave can be written as a product of two traveling waves, one oscillating at high frequency /short wavelength and one wavelength. If the medium in which the waves propagate has a dispersion relation ω(k-ck2 where c is a constant, what approximately are the wave velocities of the high frequency and low frequency part of the resulting wave? Are they the same? Show your work, and use a sketch of ω ( k ) to explain your answer.