A progressive wave has a shape (or waveform) given by the equation, $y=\frac{2}{{\left(x^2-6x+14\right)}^{3/2}}$, at the instant time t=1. Express the wave equation in terms of time t,

The given equation can be manipulated as
$y=\frac{2}{{\left(x^2-2.3x+9+5\right)}^{1/2}}$
(Making the x term a perfect slquare)
$=\frac{2}{{\left[5+(x-3{)}^2\right]}^{3/2}}$
Since the term containing x and t should always appear as a combination of the form $\mathrm{x}\pm \mathrm{vt}$; so corresponding to t=1, the expression becomes x-v. In other words v=3.
$\therefore$The wave equation can be expressed as
$y=\frac{2}{{\left[5+(x-3t{)}^2\right]}^{3/2}}$