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 of frequency $500 \, Hz$ has a velocity of $360 \, m/s$. The distance between two nearest points $60^o$ out of phase is .... $cm$.

The equation of a progressive wave is given by $x = 0.05 \cos \left( 4\pi t + \frac{\pi}{4} \right) \, m$. What is the frequency of the wave in $Hz$?

The equation of a wave travelling on a string is $y = 4\sin \frac{\pi }{2}\left( {8t - \frac{x}{8}} \right)$. If $x$ and $y$ are in $cm,$ then the velocity of the wave is:

$A$ simple harmonic progressive wave is represented by the equation $y = 8\sin 2\pi (0.1x - 2t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. At any instant,the phase difference between two particles separated by $2.0 \, cm$ in the $x$-direction is ..... $^o$.

$A$ transverse wave is represented by $y = 2 \sin(\omega t - kx) \ cm$. The value of wavelength (in $cm$) for which the wave velocity becomes equal to the maximum particle velocity is: