In a sine wave,what is the minimum distance between two particles that always have the same speed?

The figure below shows the wave $y = A \sin (\omega t - kx)$ at any instant traveling in the $+ve$ $x$-direction. What is the slope of the curve at $B$?

If a given wave has a propagation constant of $\frac{5 \pi}{7} \, rad/m$,then the phase difference between two particles having a distance difference of $\frac{49}{22} \, m$ is ..... $rad.$ (Take $\pi = \frac{22}{7}$)

$A$ progressive wave travelling along the positive $x-$ direction is represented by $y(x, t) = A \sin(kx - \omega t + \phi)$. Its snapshot at $t = 0$ is given in the figure. For this wave,the phase $\phi$ is

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

The equation of a simple harmonic wave is given by $y = 6 \sin 2 \pi (2t - 0.1x)$,where $y$ and $x$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 \ mm$ apart at any instant is (in $^{\circ}$)