The equation of a wave motion (with $t$ in seconds and $x$ in metres) is given by $y = 7\sin(7\pi t - 0.4\pi x + \frac{\pi}{3})$. The velocity of the wave will be

The equation of a progressive wave is given by $y = 6 \cos(100t - 4x)$ where $y$ is in $\mu\text{m}$, $x$ is in metre and $t$ is in second. The ratio of the maximum particle velocity to the velocity of wave is

The equation $y = A \cos^2 \left( 2\pi nt - 2\pi \frac{x}{\lambda} \right)$ represents a wave with

$A$ travelling acoustic wave of frequency $500 Hz$ is moving along the positive $x$-direction with a velocity of $300 ms^{-1}$. The phase difference between two points $x_{1}$ and $x_{2}$ is $60^{\circ}$. The minimum separation between the two points is:

$A$ transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant,among the following,choose the wrong statement.

When two sound waves travel in the same direction in a medium,the displacements of a particle located at $x$ at time $t$ are given by:
$y_1 = 0.05 \cos(0.50 \pi x - 100 \pi t)$
$y_2 = 0.05 \cos(0.46 \pi x - 92 \pi t)$
Then the velocity of the waves is..... $m/s$.