Write the definition,unit,and dimensional formula of amplitude.

The disturbance $y(x, t)$ of a wave propagating in the positive $x$-direction is given by $y = \frac{1}{1 + x^2}$ at time $t = 0$ and by $y = \frac{1}{1 + (x - 1)^2}$ at $t = 2 \ s$,where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave in $m/s$ is:

You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-vt$ or $x+vt$,i.e.,$y=f(x \pm vt)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave:
$(a)$ $(x-vt)^2$
$(b)$ $\log[(x+vt)/x_0]$
$(c)$ $1/(x+vt)$

The equation of a simple harmonic progressive wave is given by $Y = a \sin 2 \pi (b t - c x)$. The maximum particle velocity will be twice the wave velocity if:

$A$ pulse on a string is shown in the figure. $P$ is a particle of the string. State which of the following is incorrect.

Two waves are represented by the equations, $y_1 = a \sin(\omega t + kx + 0.57)$ and $y_2 = a \cos(\omega t + kx)$, where $x$ is in metre and $t$ is in second. What is the phase difference between them? $(\pi = 3.14)$