The equation of a simple harmonic progressive wave is given by $Y = a \sin 2 \pi (b t - c x)$. The maximum particle velocity will be twice the wave velocity if:

For the wave $y(x, t) = 3.0 \sin (36 t + 0.018 x + \pi / 4)$,plot the displacement $(y)$ versus time $(t)$ graphs for $x = 0, 2$ and $4 \; cm$. What are the shapes of these graphs? In which aspects does the oscillatory motion in a travelling wave differ from one point to another: amplitude,frequency,or phase?

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 .... $Hz$.

The equation of wave motion is $Y = 6 \sin (12\pi t - 0.02\pi x + \pi/3)$ where $x$ is in metre and time in second. The velocity of the wave is (in $\text{ m/s}$)

$A$ plane wave is represented by $x = 1.2 \sin(314t + 12.56y)$,where $x$ and $y$ are distances measured in meters and $t$ is time in seconds. This wave has:

In a wave,the path difference corresponding to a phase difference of $\phi$ is