$A$ travelling wave is described by the equation $y(x, t) = 0.05 \sin(8x - 4t) \; m$. The velocity of the wave is $..... \; m/s$ [all the quantities are in $SI$ units].

The phase difference between two points separated by $1 \ m$ in a wave of frequency $120 \ Hz$ is $90^o$. The wave velocity is .... $m/s$.

$A$ wave is given by $Y = 3 \sin 2 \pi \left( \frac{t}{0.04} - \frac{x}{0.01} \right)$ where $Y$ is in $cm$. The frequency of the wave and the maximum acceleration will be $(\pi^2 = 10)$.

If the equation of a progressive wave is given by $y = 3 \cos \pi (100 t - x) \text{ cm}$,then what is the wavelength of the wave in $\text{cm}$?

The equation of a transverse wave is given by $y=0.05 \sin \pi(2 t-0.02 x)$,where $x, y$ are in metre and $t$ is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively

$A$ wave in a string has an amplitude of $2\, cm$. The wave travels in the $+ve$ direction of $x-$axis with a speed of $128\, m/s$ and it is noted that $5$ complete waves fit in $4\, m$ length of the string. The equation describing the wave is