wave speed
When you watch a wave cross a pond or run along a rope, the wave speed is simply how fast the pattern, the crest, travels. The question it answers is: how quickly does the disturbance get from one place to another?
The wave speed v is the distance the wave pattern travels per unit time, in metres per second. It is tied to wavelength and frequency by v = f lambda: in one period T = 1/f the wave advances exactly one wavelength, so v = lambda / T = f lambda. Crucially, the speed is set by the medium, not by the source. For a wave on a string, v = sqrt(T/mu), where T is the tension and mu is the mass per unit length, so tighter or lighter strings carry waves faster.
Because the medium fixes v, if you change the frequency then the wavelength adjusts to keep v = f lambda true. Play a higher note on a guitar string and the wavelength shrinks, not the speed. An honest caveat: in some media the speed does depend slightly on frequency (this is called dispersion, and it is why a prism splits white light into colours), but for many everyday waves the speed is nearly constant.
On a guitar string under tension T = 80 N with mass per length mu = 0.005 kg/m, waves travel at v = sqrt(80/0.005) = sqrt(16000), about 126 m/s.
The medium sets the wave speed; the source sets the frequency; wavelength adjusts so v = f lambda.
Wave speed is the speed of the pattern, not of the particles. The rope's particles just jiggle in place, usually far slower than the wave races along.