Question

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?

• A. $y=A\sin (kx-\omega t)$
• B. $y=A{\sin }^2(kx-\omega t)$
• C. $y=A\sin (k^2{x}^2-{\omega }^2{t}^2)$
• D. $y=A\sin (kx+\omega t+\frac{\pi }{10})$

Answer 1

The correct option is C $y=A\sin (k^2{x}^2-{\omega }^2{t}^2)$

The displacement $\left(y\right)$ represented as function of $x$ and $t$ of type $(ax\pm bt)$ represent a wave function.
$\Rightarrow y(x,t)=f(ax\pm bt)$
If any function is represented by non-linear terms of $x$ or $t$ or both, it does not represent a wave.
$\therefore y=A\sin (k^2{x}^2-{\omega }^2{t}^2)$ does not represent a wave motion.
Hence, option $\left(c\right)$ is correct answer.