$A$ wave travelling in the $+ve$ $x$-direction having displacement along $y$-direction as $1\, m$,wavelength $2\pi\, m$,and frequency of $\frac{1}{\pi}\ Hz$ is represented by

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 $m/s$)

$A$ 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 ..... $^o$.

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.
$(i) \, y = 5 \cos (4x) \sin (20t)$
$(ii) \, y = 4 \sin (5x - t/2) + 3 \cos (5x - t/2)$
$(iii) \, y = 10 \cos (252\pi t) \cos (250\pi t)$
$(iv) \, y = 100 \cos (100\pi t + 0.5x)$
State which of these represent:
$(a)$ a travelling wave along $-x$ direction
$(b)$ a stationary wave
$(c)$ beats
$(d)$ a travelling wave along $+x$ direction.
Give reasons for your answers.

The equation of wave motion is $Y = 5 \sin (10 \pi t - 0.02 \pi x + \pi / 3)$ where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is (in $m/s$)

$A$ transverse wave is represented by $y = \frac{10}{\pi} \sin \left( \frac{2\pi}{T}t - \frac{2\pi}{\lambda}x \right)$. For what value of the wavelength is the wave velocity twice the maximum particle velocity (in $cm$)?