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 $60 \ cm$?

$A$ 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?

$A$ progressive wave is represented by $y=12 \sin (5 t-4 x) \ cm$. On this wave,how far away are the two points having a phase difference of $90^{\circ}$?

The equation of a progressive wave is given by $y = 4 \sin \left( \pi \left( \frac{t}{5} - \frac{x}{9} \right) + \frac{\pi}{6} \right)$. Which of the following is correct?

The equation of a progressive wave is given by $x = 1.2 \sin(314t + 12.56y)$. What are the wavelength and the direction of the wave?

$y=3 \sin \pi\left(\frac{t}{2}-\frac{x}{4}\right)$ represents an equation of a progressive wave,where $t$ is in $s$ and $x$ is in $m$. The distance travelled by the wave in $5 \,s$ is (in $\,m$)