Every wave -- whatever its type -- can be described by a common set of quantities: amplitude (A), the largest displacement any particle of the medium undergoes from its rest position; wavelength (λ), the distance between two successive particles that are in exactly the same phase of vibration; period (T), the time for one particle to complete a full vibration; frequency (n = 1/T), the number of vibrations per second; and wave velocity (v), the distance the disturbance itself advances per unit time. Because a wave covers exactly one wavelength in exactly one period, these combine into the single most-used relation of wave motion, v=nλ.
A wave is described as doubly periodic: at a fixed location it repeats in TIME (period T), and at a fixed instant it repeats in SPACE (wavelength λ). A crucial consequence of v=nλ is that for a wave travelling through a given medium the speed v stays fixed, so a higher frequency always means a shorter wavelength; and when a wave crosses from one medium into another, its FREQUENCY (set by the source) never changes -- it is the speed and wavelength that adjust instead. For a mechanical wave to exist at all, the medium must be continuous and elastic, must possess inertia, and must have negligible frictional losses.