<Dd> v p = ω k . (\ displaystyle v_ (\ mathrm (p)) = (\ frac (\ omega) (k)).) </Dd> <P> To understand where this equation comes from, consider a basic sine wave, A cos (kx − ωt). After time t, the source has produced ωt / 2π = ft oscillations . After the same time, the initial wave front has propagated away from the source through space to the distance x to fit the same number of oscillations, kx = ωt . </P> <P> Thus the propagation velocity v is v = x / t = ω / k . The wave propagates faster when higher frequency oscillations are distributed less densely in space . Formally, Φ = kx − ωt is the phase . Since ω = − dΦ / dt and k = + dΦ / dx, the wave velocity is v = dx / dt = ω / k . </P> <P> Since a pure sine wave cannot convey any information, some change in amplitude or frequency, known as modulation, is required . By combining two sines with slightly different frequencies and wavelengths, </P>

Speed of a wave in terms of k and w
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