The equation of a travelling wave is $y = 60 \cos (1800t - 6x)$,where $y$ is in microns,$t$ is in seconds,and $x$ is in metres. The ratio of maximum particle velocity to the velocity of wave propagation is:

The speed of a wave in a medium is $960 \, m/s$. If $3600$ waves pass through a point in the medium in $1 \, minute$,what is the wavelength of the wave in $meters$?

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 $t = 5 \ s$?

The equation of a wave is given by (all quantities expressed in $M.K.S.$ units) $Y = 5 \sin(10\pi t - 0.1\pi x)$ along the $x$-axis. The phase difference between two points separated by a distance of $10 \ m$ along the $x$-axis is:

An observer standing near the sea shore observes $54$ waves per minute. If the wavelength of the water wave is $10 \ m$,then the velocity of the water wave is .... $m/s$.

$A$ 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: