$A$ transverse wave is described by the equation $y = y_0 \sin 2 \pi \left( \nu t - \frac{x}{\lambda} \right)$. The maximum particle velocity is equal to four times the wave velocity if $\lambda =$

$A$ boat at anchor is rocked by waves whose crests are $100 \,m$ apart and velocity is $25 \,m/s$. The boat bounces up once in every (in $\,s$)

$A$ particle performs $S.H.M.$ of amplitude $A$ and the wave has a wavelength $\lambda$. If $V$ is the wave velocity and $\nu$ is the maximum particle velocity,then they are related as:

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 $t = 5 \ s$?

$A$ transverse wave given by $y=2 \sin (0.01 x+30 t)$ moves on a stretched string from one end to another end in $0.5 \ s$. If $x$ and $y$ are in $cm$ and $t$ is in $s$,then the length of the string is: (in $m$)

The displacement of a particle in a medium is $y = 10^{-4} \sin(100t + 20x + \frac{\pi}{3}) \ m$,where $t$ is in seconds and $x$ is in metres. The speed of the wave is (in $m/s$)