SPEED OF A WAVE MOTION

SPEED OF A WAVE MOTION
The speed of a mechanical (elastic) wave, is clearly expected to depend upon the properties of the medium through which the wave is travelling. The medium could be a solid, liquid or a gas. All media are characterized by their physical properties, like mass, density, elasticity, and temperature. Any alternation, in the properties of the medium, would cause a change in the speed of propagation of a
wave through it. For example, an increase, in the tension of a spring, increases the wave speed through it.

Hence one can say that the speed, of a (given type of) mechanical wave, in a medium, depends upon the properties of the medium. For given type of waves (in a given medium), this speed, however does not change with a change in the characteristics (amplitude, wave length or frequency) of the wave. For example, the speeds of different types of sound waves, infrasonic, audible or ultrasonic, in a given medium, are all given by

v = √(E/ρ)

where E is the (appropriate) elastic constant and ρ is the density of the medium.
The speed is thus dependent only on the properties of the medium. It is interesting to note that the speed of propagation of electromagnetic waves is also determined by the ‘characteristics’ of the medium through which they are propagating.
EM. waves, as we know, are a ‘combination’ of the oscillations of electric and magnetic fields in mutually perpendicular directions. The relevant ‘properties’ of the medium, determining their speed of propagation, are the ‘permittivity’ and the ‘permeability ‘ of the medium.
In vacuum, the speed of propagation (c) of all types of e.m. waves, is given by

c = 1/√(μoεo)

Here μo = permeability of vacuum and εo = permittivity of vacuum.
In any other material medium, the speed of propagation (v ) of e.m. waves, is given by

v = 1/√(με)

where μ= permeability of the medium and ε = permittivity of the medium. The speed of propagation of these different waves, is therefore not quite the same and this leads to the well known ‘dispersion’ phenomenon – resulting in the formation of ‘spectra’.