9.2 One Dimensional, Linear , Progressive Harmonic Wave and its equation
Consider a transverse wave, ( for convenience ) propagating along the + ve X axis as shown above.
Let the wave originate at t = 0 from the point 'O'.
The S.H.M. of 'O' is given by
f0 = r sin (wt )
The particle at 'P' receives the energy from 'O' after time x / v sec. Later S.H.M. of 'p' is given by
This equation for any arbitrary particle 'p' through
which the wave passes is called the Wave equation. Essentially the
wave equation must represent S.H.M. of each and every particle through
which it propagates.
represents both transverse and longitudinal waves.
Alternately, f = r cos 2p also represents wave equation albeit with shift of crest / trough
or compression / rarefaction by
distance compared to equation in (1).
A wave traveling along -ve X - axis will be represented by,
As in S.H.M. energy of wave is proportional to the square of amplitude 'r' of
9.1 Tranverse and Longitudinal Waves
9.2 Equation of Linear, Progressive, Harmonic Waves