Two waves are represented by the equations $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$. The first wave is .....

$A$ plane wave is described by the equation $y = 3 \cos \left( \frac{x}{4} - 10t - \frac{\pi}{2} \right)$. The maximum velocity of the particles of the medium due to this wave is

The equation of a wave is given by $Y = 10^{-2} \sin 2 \pi (160 t - 0.5 x + \frac{\pi}{4})$,where $x$ and $Y$ are in $m$ and $t$ is in $s$. The speed of the wave is $..... \, km \, h^{-1}$.

The equation of a simple harmonic wave is given by $y = 3 \sin \frac{\pi}{2}(50t - x)$,where $x$ and $y$ are in metres and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is

$A$ 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 figure represents the instantaneous picture of a transverse harmonic wave traveling along the negative $x$-axis. Choose the correct alternative$(s)$ related to the movement of the nine points shown in the figure. The points moving upward is/are