What is Travelling wave, celerity? — Physics

Definition 5.5 University Physics — Year 1 · Chapter 5 — Signal Propagation: Travelling and Standing Waves

A signal $s(x, t)$ defined along an axis is a travelling wave moving in the $+x$ direction at celerity $c$ if

s(x, t) = f\!\left(t - \frac{x}{c}\right) = F(x - ct)

for some function $f$ (or $F$ ): the shape is carried along unchanged, shifted by $c\,\Delta t$ in time $\Delta t$ . A wave moving toward $-x$ is $g(t + x/c)$ . A medium in which every shape propagates undeformed at the same $c$ is non-dispersive.

The double periodicity of a sinusoidal travelling wave: a snapshot at fixed time repeats every wavelength and slides at speed c; the signal at a fixed point repeats every period T, with = cT. — The double periodicity of a sinusoidal travelling wave: a snapshot at fixed time repeats every wavelength $\lambda$ and slides at speed $c$ ; the signal at a fixed point repeats every period $T$ , with $\lambda = cT$ .

Examples

Example 5.7 (Celerities)

Sound in air, $340\,\mathrm{m}/\mathrm{s}$ : thunder $3\,\mathrm{s}$ after the flash puts the strike $1\,\mathrm{km}$ away. Sound in water, $1500\,\mathrm{m}/\mathrm{s}$ ; in steel, $5000\,\mathrm{m}/\mathrm{s}$ . Transverse waves on a string of tension $F$ and mass per unit length $\mu$ : $c = \sqrt{F/\mu}$ , as dimensional analysis predicted (Exercise 1.5) — $140\,\mathrm{m}/\mathrm{s}$ for a guitar string. Light in vacuum, $c = 3.00 \times 10^{8}\,\mathrm{m}/\mathrm{s}$ ; in glass, $c/n$ . The celerity is a property of the medium, not of the source: a whisper and a shout arrive together.

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