Question

Which of the following function correctly represent the travelling wave equation for finite values of $x$ and $t$?

• A. $y=x^2-t^2$
• B. $y=log(x^2-t^2)-log(x-t)$
• C. $y=e^{2x}\sin t$
• D. $y=\cos x^2\sin t$

Answer 1

The correct option is B $y=log(x^2-t^2)-log(x-t)$

As we know that, the equation of travelling wave is given by
$y=f(x-vt)$ $+vex$ direction
$y=f(x+vt)$ $-vex$ direction
$\left(a\right)y=x^2-t^2$
$=(x-t)(x+t)$
$y=\left(y_1\right)\left(y_2\right)$
It is the multiplication of two travelling wave which is not a condition of a travelling wave.
$\left(b\right)y=\cos x^2\sin t$
$\to$ It is the equation of standing wave. So, it is not a travelling wave
$\left(c\right)y=$log$(x^2-t^2)-$log$(x-t)$
$=$log$\frac{(x^2-t^2)}{(x-t)}$
$y=$log$(x+t)$
Which represents the equation of travelling wave.
$\left(d\right)y=e^{2x}\sin t$
This equation is not in the form of $f(x\pm vt).$So, this is not a travelling wave.

Final answer: $\left(c\right)$