The displacement $y$ of a particle on a straight line is given by $y = f(x, t)$, as a function of time.…
The displacement $y$ of a particle on a straight line is given by $y = f(x, t)$, as a function of time. Which of the following functions does not represent wave motion?
$y = A \sin (kx - \omega t)$
$y = A \sin^2 (kx - \omega t)$
$y = A \sin (k^2 x^2 - \omega^2 t^2)$
$y = A \sin \left(kx + \omega t + \frac{\pi}{10}\right)$
Solution
All functions of $x$ and $t$ of type $(ax \pm bt)$ represent a wave.
So, $y = A \sin (k^2x^2 - \omega^2t^2)$ does not represent wave motion.