The equation of a wave is $Y = 6 \sin(12 \pi t - 0.02 \pi x + \frac{\pi}{3})$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is: (in $m/s$)

$A$ sinusoidal wave of frequency $500 \,Hz$ has a speed of $350 \,m/s$. The phase difference between two displacements at two points separated by a distance of $1 \,m$ is ...........

The wave equation is $y = 0.30 \sin (314t - 1.57x)$ where $t, x$ and $y$ are in second,meter and centimeter respectively. The speed of the wave is ..... $m/s$.

$A$ sound of frequency $480 \,Hz$ is emitted from a stringed instrument. The velocity of sound in air is $320 \,m/s$. After completing $180$ vibrations, the distance covered by the wave is: (in $\,m$)

The wave function of a pulse is given by $y = \frac{5}{(4x + 6t)^2}$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of the pulse is ......... $m/s$.

The graph between wave number $(\bar \nu)$ and angular frequency $(\omega)$ is