Velocity of Waves in Different Media

Everyday experience shows that wave velocity is not a universal constant but depends entirely on the medium a wave is travelling through. A vivid illustration: if a hammer is struck once on a long steel rail and a listener presses an ear against the rail some distance away, two distinct sounds are heard at two different instants -- first the sound that has travelled through the rail itself (a solid medium), and only afterward the sound that has travelled the same distance through the air (a gaseous medium) -- since sound moves markedly faster through the solid rail than through air. This section derives, from first principles using Newtonian mechanics, exactly how fast a wave travels in two distinct physical situations: the velocity of a transverse wave travelling along a stretched string, and the velocity of a longitudinal wave travelling through a general elastic medium (solid, liquid or gas). Both derivations reveal the same underlying pattern -- wave speed always depends jointly on an elastic property of the medium (which supplies the restorin …