A transverse wave travelling on a stretched string is represented by the equation, $y=\frac{2}{(2x-6.2t{)}^2+20}$; where $x \text{and} y$ are in $\mathrm{meter}$ and $t$ is in $\mathrm{second}$, Then,

In the wave equation, $y=A\sin 2\mathrm{\pi }\left(\frac{x}{a}-\frac{t}{b}\right)$,

Corresponding to the $y-t$ graph of a transverse harmonic wave shown in the figure, choose the correct options at same position.

The figure shows a snap photograph of a vibrating string at $t=0$ .The particle $P$ is observed moving up with velocity $20\sqrt{3}\mathrm{cm} {\mathrm{s}}^{-1}$. The tangent at $P$ makes an angle $60°$ with $x$-axis.

(a) Find the direction in which the wave is moving.
(b) Write the equation of the wave.
(c) Find the total energy carried by the wave per cycle of the string. Assume that the mass per unit length of the string is $50 \mathrm{g} {\mathrm{m}}^{-1}$.

A long string, having a cross-sectional area $0.80 {\mathrm{mm}}^2$ and density $12.5 \mathrm{g} {\mathrm{cm}}^{-3}$, is subjected to a tension of $64 \mathrm{N}$ along the positive $x$-axis. One end of this string is attached to a vibrator at $x=0$, moving in the transverse direction at a frequency of $20 \mathrm{Hz}$. At $t=0$, the source is at maximum displacement, $y=1.0 \mathrm{cm}$.

(a) Find the speed of the wave traveling on the string.
(b) Write the equation for the wave.
(c) What is the displacement of the particle of the string at $x=50 \mathrm{cm}$ at time, $t=0.05 \mathrm{s}$?
(d) What is the velocity of this particle at this instant?

One end of each of two identical springs, each of force constant $0.5 \mathrm{N} {\mathrm{m}}^{-1}$, are attached on the opposite sides of a wooden block of mass $0.01 \mathrm{kg}$. The other ends of the springs are connected to separate rigid supports such that the springs are unstretched and are collinear in a horizontal plane. To the wooden piece is fixed a pointer which touches a vertically moving plane paper. The wooden piece kept on a smooth horizontal table is now displaced by $0.02 \mathrm{m}$ along the line of springs and released. If the speed of paper is $0.1 \mathrm{m} {\mathrm{s}}^{-1}$, find the equation of the path traced by the pointer on the paper and the distance between two consecutive maxima on this path.