During the propagation of transverse waves:

Figure shows an incident pulse $P$ reflected from a rigid support. Which one represents the reflected pulse correctly?

A transverse pulse is given as, $y=\frac{10}{10x-\pi t}$ where, $x$ and $y$ are in $\mathrm{cm}$ and $t$ is in $\sec$.

Assertion: The frequency of the pulse is $\frac{1}{20} \mathrm{Hz}$.
Reason: We can write this equation as, $y=\frac{A}{kx-\omega t}$ where,$A\text{,} k$ and $\omega$ are the amplitude, wave number and angular frequency of pulse.

The respective displacements (in $\text{cm}$) of two particles of a medium disturbed by a wave propagation at $x_1=0$ and $x_2=1 \text{cm}$ are given by the equations:$y_1=2\sin 3\text{πt}$
$y_2=2\text{sin}(3\pi t-\pi /8)$

The speed of the wave is

Consider a plane progressive wave propagating along negative $x$-direction whose frequency is $f$. At $t=t_0$ the displacement associated with the wave is given by the following equation:

$y\left(x, t=t_0\right)=A \cos kx$

Displacement associated with the wave as a function of $x$ at $t=2t_0$ can be represented by equation.