Is y = a log(x - vt) a traveling wave?

[Amith2006]

Sir,
Does the equation,
y = a[log(x – vt)]
Represent a traveling wave?
I think the answer is No, because it is not a harmonic function. Is it right?

 

[Reshma]

Why don't you just plug it in the d'Alembertian operator and see if both sides are equal?
$$\Box = \nabla^2 - { 1 \over c^2} \frac{ \partial^2} { \partial t^2}$$

 

[maverick280857]

Why don't you just plug it in the d'Alembertian operator and see if both sides are equal?
$$\Box = \nabla^2 - { 1 \over c^2} \frac{ \partial^2} { \partial t^2}$$

Yes with $\Box^{2}y = 0$ and the c replaced by v of course so its really a non-relativistic d'Alembertian.

But more than that you should know what CLASS of solutions can be solutions of the wave equation...harmonic functions is a subset of this class.