Definition

Wave speed is how fast a wave moves from one place to another, and it depends on the medium the wave travels through, not on how big or how frequent the wave is; it equals frequency times wavelength, $v = f\lambda$, in meters per second, so shouting louder does not make sound travel faster, since all sounds in the same air move at the same speed. Sound travels at about $343\ \text{m/s}$ in air at $20^\circ\text{C}$, faster in water ($1{,}480\ \text{m/s}$) and faster still in steel, while light travels at $3.00 \times 10^8\ \text{m/s}$ in a vacuum and slightly slower in glass or water. Wave speed is the phase velocity $v = \omega/k = f\lambda$, set by the medium's restoring force and inertia: $v = \sqrt{T/\mu}$ for a stretched string, $v = \sqrt{B/\rho}$ for sound in a fluid, and $v = \sqrt{\gamma RT/M}$ for an ideal gas, which gives $343\ \text{m/s}$ for air at $293\ \text{K}$; electromagnetic waves in vacuum travel at $c = 1/\sqrt{\mu_0\varepsilon_0} = 2.998 \times 10^8\ \text{m/s}$, and in a dispersive medium the group velocity $d\omega/dk$ that carries energy and information can differ from the phase velocity.