Question

Which of the folLowing function correctly represents the wave equation:

• A. y = x -t²
• B. y = coc x²sint
• C. y = log(x²-t²)-log(x-t)
• D. y = e^2xsint

Answer 1

Answer: (C)

y = log(x²-t²)-log(x-t)

Answer 2

A function represents correct wave equation if it satisfies the condition

$\frac{\partial^{2}y}{\partial x^{2}} = \frac{1}{V}\frac{\partial^{2}y}{\partial x^{2}}$

where V= $\frac{\partial x}{\partial t}$ is wave speed,

y = log $\frac{x^{2} - t^{2}}{x - t}$ = log(x + t)

$\frac { \partial y } { \partial x } = \frac { 1 } { ( x + t ) }$ $\frac{\partial^{2}y}{\partial x^{2}} = \frac{1}{(x + t)^{2}}$

and $\frac{\partial^{2}y}{\partial t^{2}} = - \frac{v^{2}}{(x + t)}$

⇒ $\frac{\partial^{2}y}{\partial x^{2}} = \frac{1}{v^{2}}\frac{\partial^{2}y}{\partial t^{2}}$That is general form of wave equation and only wave equation given in (3) satisfies it.