The Speed of a Travelling Wave

It is essential to distinguish the wave speed $v$ from the frequency $f$ or wavelength $\lambda$ individually: while $v=f\lambda$ connects the three quantities kinematically, the speed $v$ at which a mechanical wave travels through a given medium is fixed entirely by the medium's own mechanical properties -- specifically, by a ratio of an elastic property (which supplies the restoring force) to an inertial property (which supplies the mass to be restored) -- and does NOT depend on the frequency or amplitude of the particular wave passing through it. On general dimensional grounds, the speed of a mechanical wave always takes the form $v = \sqrt{\frac{\text{elastic property of the medium}}{\text{inertial property of the medium}}}$ Because the medium fixes $v$, a source that vibrates at some chosen frequency $f$ forces the medium to carry a wave of wavelength $\lambda=v/f$ -- change the source's frequency and the wavelength adjusts correspondingly, but the wave's speed through that same medium stays the same. The next two sections work ou …