$A$ triangular pulse moving at $2 \ cm/s$ on a rope approaches an end at which it is free to slide on a vertical pole. What is the particle speed at the free end at $\frac{3}{4} \ s$ from the instant shown? (in $cm/s$)

Give the definition,equation,and unit for wavelength and wave number for a wave.

Two waves are represented by the equations: $y_1 = a \sin(\omega t + kx + 0.57) \ m$ and $y_2 = a \cos(\omega t + kx) \ m$,where $x$ is in $meters$ and $t$ is in $seconds$. The phase difference between them is ..... $radian$.

If the equation of a transverse wave is $Y = 2 \sin(kx - 2t)$,then the maximum particle velocity is .... $units$.

$A$ wave is represented by the equation $y = (0.02 \ m) \sin (5 \pi x - 20 t)$. The minimum distance between two particles always having the same speed is: (Assume $x$ and $t$ are in $SI$ units) (in $m$)

$A$ transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \text{ cm/s}$. The wavelength of the wave is $0.5 \text{ m}$ and its amplitude is $10 \text{ cm}$. At a particular time $t$,the snapshot of the wave is shown in the figure. The velocity of point $P$ when its displacement is $5 \text{ cm}$ is: