The equation of a progressive wave is $y = a \sin \left( \frac{\pi}{2}x - 200\pi t \right)$. The frequency of the wave will be .... $Hz$.

$A$ 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: ... $s$

You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-vt$ or $x+vt$,i.e.,$y=f(x \pm vt)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave:
$(a)$ $(x-vt)^2$
$(b)$ $\log[(x+vt)/x_0]$
$(c)$ $1/(x+vt)$

The equation of a simple harmonic wave is given by $y = 6 \sin 2 \pi (2t - 0.1x)$,where $y$ and $x$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 \ mm$ apart at any instant is (in $^{\circ}$)

When a sound wave of wavelength $\lambda$ is propagating in a medium,the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is:

$A$ wave equation which gives the displacement along the $Y$ direction is given by the equation $y = 10^4 \sin(60t + 2x)$,where $x$ and $y$ are in metres and $t$ is time in seconds. This represents a wave: