Demonstrate that any differentiable function `f( f+ alphax)`, where `alpha` is a constant, provides a solution of wave equation. What is the physical meaning of the constant `alpha` ?

Explanation

This follows on actually putting
`xi=f(t+alphax)`
in the wave eqaution `(delta^(2)xi)/( deltax^(2))=(1)/(v^(2))(delta^(2)xi)/(deltat^(2))`
`(` We have written the one dimensional form of the wave equation. `)`. Then
`(1)/(v^(2))f^('') (t+alphax)=alpha^(2)f^('') (t+alphax)`
so the wave equation is satisfied if
`alpha=+- (1)/(v^('))`
That is the physical meaning of the constant `alpha`.