Understanding the One Dimensional Wave Equation

[OnceKnown]

Homework Statement

Given that the the One Dimensional wave equation is $\frac{∂^{2}y(x,t)}{∂x^{2}}$ = $\frac{1}{v^{2}}$ $\frac{∂^{2}y(x,t)}{∂t^{2}}$ is y(x,t) = ln(b(x-vt)) a solution to the One Dimensional wave equation?

Homework Equations

Shown above.

The Attempt at a Solution

So my Professor stated that yes, it was a solution to the One Dimensional Wave equation, but I am confused on the process to get this answer. Do we plug the ln(b(x-vt)) into the y(x,t) of the equation and then using partial differentiation to solve in terms of "x" and "t" and see if they match the original equation?

 

[Sunil Simha]

Do we plug the ln(b(x-vt)) into the y(x,t) of the equation and then using partial differentiation to solve in terms of "x" and "t" and see if they match the original equation?

Yes, that is a right method.

 

[Sunil Simha]

Do we plug the ln(b(x-vt)) into the y(x,t) of the equation and then using partial differentiation to solve in terms of "x" and "t" and see if they match the original equation?

Yes, that is a right method.