Propagation speed

A harmonic wave advances: its profile, that cosine curve, moves rigidly through space as time passes. The propagation speed $v$ measures precisely how fast the profile moves. The most direct way to obtain it is to observe that, in the time of one period $T$, the wave advances by exactly one wavelength $\lambda$: it covers a distance $\lambda$ in a time $T$.

Key formula — Propagation speed

$\ev{v = \frac{\lambda}{T} = \lambda\,f = \frac{\omega}{k}}$

The three expressions are equivalent: from $f = 1/T$ it follows that $\lambda/T = \lambda f$, and substituting $\lambda = 2\pi/k$ and $T = 2\pi/\omega$ gives $\lambda/T = \omega/k$. They are just three viewpoints on the same quantity, convenient depending on whether you know the period and wavelength, or the angular frequency and wave number.

What actually moves

The speed $v$ is the speed at which the wave’s profile moves, not the speed of the particles of the medium. Each particle merely oscillates back and forth about its own equilibrium position, never travelling along with the wave. What propagates is the shape of the disturbance — and with it the energy — while the matter stays put.

Links

Topics: Onde Concepts: Onda armonica

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