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

For a wave equation $y = 8 \sin 2\pi (0.1x - 2t) \, cm$,find the phase difference in $^\circ$ between two particles separated by a distance of $2 \, cm$.

For the harmonic travelling wave $y = 5 \cos 2\pi (10t - 0.008x + 3.5)$ where $x$ and $y$ are in $cm$ and $t$ is in seconds. What is the phase difference between the oscillatory motion at two points separated by a distance of:
$(a)$ $4 \ m$
$(b)$ $0.5 \ m$
$(c)$ $\frac{\lambda}{2}$
$(d)$ $\frac{3\lambda}{4}$ (at a given instant of time)
$(e)$ What is the phase difference between the oscillation of a particle located at $x = 100 \ cm$,at $t = T \ s$ and $t = 5 \ s$?

Which of the following waves has the largest wave speed?

The equation of a wave is given as $y = 0.07 \sin (12\pi x - 3000\pi t)$. Where $x$ is in $m$ and $t$ is in $s$,then the correct statement is:

$A$ transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \text{ cm/s}$. The wavelength of the wave is $0.5 \text{ m}$ and its amplitude is $10 \text{ cm}$. At a particular time $t$,the snapshot of the wave is shown in the figure. The velocity of point $P$ when its displacement is $5 \text{ cm}$ is: