which of the following function corrtly represent the traveling wave equation for finite values of x and t ?

Options

A. `y = x^(2) - t^(2)`
B. `y = cos x^(2) sin t`
C. `y = log(x^(2) - t^(2)) - log (x-t)`
D. `y= e^(2x) sin t`

Answer

C

Explanation

For any equation to be wave equation.
`(d^(2)y)/(dx^(2)) = 1/v^(2) (d^(2)y)/(dt^(2))`
In the given option `y = log ((x^(2) - t^(2))/(x-t)) = log (x+t)`
`therefore log a - log b = log a/b`
`(dy)/(dx) = 1/(x+t)`
`(d^(2)y)/(dx^(2)) = -1/(x+t)^(2)`
and `(dy)/(dx) = 1/(x +t)` or `(d^(2)y)/(dt^(2)) = -1/(x+t)^(2)`
`rArr ((d^(2)y)/(dx^(2)))/((d^(2)y)/(dx^(2))) = + ve` constant, hence proves to be a wave equation.