The relation between frequency '$n$',wavelength '$\lambda$',and velocity of propagation '$v$' of a wave is:

The figure represents the instantaneous picture of a transverse harmonic wave travelling along the negative $x$-axis. Identify the correct statement(s) related to the movement of the points shown in the figure. The points moving opposite to the direction of propagation (i.e., moving in the negative $y$-direction) are:

For a wave equation $Y = Y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right) \text{ cm}$,the condition for the maximum particle velocity to be four times the wave velocity is:

$A$ transverse wave is travelling along a stretched string from right to left. The figure shown represents the shape of the string at a given instant. At this instant,

$A$ transverse wave is represented by the equation $y=2 \sin (30 t-40 x)$ where the measurements of distances are in meters,then the velocity of propagation is (in $ms^{-1}$)

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