I am wondering if group velocity can defined only for waves with very close wavenumber? I see a number of simulations which shows the superposition of two waves with slighlty different wavenumber and angular frequency, and a train of wave pulses is produced. The group velocity is then (w2-w1)/(k2-k1). But what if it is two waves of very different wavenumber? And also, for waves that is composed of a range of values of k, where shall I evluate the group velocity i.e. the derivative dw/dt at?