The equation of wave motion is $Y = 6 \sin (12\pi t - 0.02\pi x + \pi/3)$ where $x$ is in metre and time in second. The velocity of the wave is (in $\text{ m/s}$)

$A$ transverse wave of frequency $500 \,Hz$ and speed $100 \,m/s$ is travelling in the positive $x$-direction on a long string. At time $t=0 \,s$,the displacements at $x=0.0 \,m$ and at $x=0.25 \,m$ are $0.0 \,m$ and $0.02 \,m$,respectively. The displacement at $x=0.2 \,m$ at $t=5 \times 10^{-4} \,s$ is ............ $m$.

The amplitude of a wave represented by the displacement equation $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$ will be

When a wave travels in a medium,the particle displacement is given by $y(x, t) = 0.03 \sin \pi (2t - 0.01x)$,where $y$ and $x$ are in meters and $t$ is in seconds. The phase difference,at a given instant of time,between two particles $25 \ m$ apart in the medium is:

The displacement $y$ of a wave travelling in the $x$-direction is given by $y = 10^{-4} \sin(600t - 2x + \frac{\pi}{3})$ metres,where $x$ is expressed in metres and $t$ in seconds. The speed of the wave motion,in $m \ s^{-1}$,is

$A$ wave travelling along the $x$-axis is described by the equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and the time period of the wave are $0.08 \ m$ and $2.0 \ s$ respectively,then $\alpha$ and $\beta$ in appropriate units are: