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 = cosx^(2) sint`
C. `y = log(x^(2) - t^(2)) - log(x -t)`
D. `y = e^(2x) sin t`

Answer

C

Explanation

Analyzing option ("C") we have
`y = log(x^(2) - t^(2))/(x - t) = log (x + t)`
` [As log a - lob b = log(a)/(b)]
implies (partialy)/(partialx) = (1)/((x + t))`
implies `(partial^(2)y)/(partialx^(2)) = - (1)/((x + t)^(2))`
`(partialy)/(partialt) = ((partialx//partialt))/((x + t)) = (v)/((x + t))`
implies `(partial^(2)y)/(partialt^(2)) = -(v^(2))/((x + t)^(2))`
implies `(partial^(2)y)/(partialx^(2)) = (1)/(v^(2))(partial^(2)y)/(partialt^(2))`