The equation of a progressive wave is $y = 0.02 \sin 2\pi \left[ \frac{t}{0.01} - \frac{x}{0.30} \right]$. Here $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of propagation of the wave is .... $ms^{-1}$.

Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent a travelling wave.

$A$ transverse harmonic wave on a string is described by $y(x, t) = 3.0 \sin (36t + 0.018x + \pi/4)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The positive direction of $x$ is from left to right.
$(a)$ Is this a travelling wave or a stationary wave? If it is travelling,what are the speed and direction of its propagation?
$(b)$ What are its amplitude and frequency?
$(c)$ What is the initial phase at the origin?
$(d)$ What is the least distance between two successive crests in the wave?

At a moment in a progressive wave,the phase of a particle executing $S.H.M.$ is $\frac{\pi}{3}$. What will be the phase of a particle $15 \ cm$ ahead at a time $\frac{T}{2}$ later,if the wavelength is $60 \ cm$?

What are called progressive waves? What is called a wave equation? Write the wave equation for a progressive harmonic transverse wave propagating and explain it by drawing graphs.

$A$ progressive wave moving along the $x$-axis is represented by $y = A \sin \left[ \frac{2 \pi}{\lambda} (vt - x) \right]$. The wavelength $\lambda$ at which the maximum particle velocity is $3$ times the wave velocity is: