Wave equations of two particles are given by $y_1 = a \sin(\omega t - kx)$ and $y_2 = a \sin(kx + \omega t)$. Then:

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 $m/s$)

The phase difference between two points separated by $1 \ m$ in a wave of frequency $120 \ Hz$ is $90^o$. The wave velocity is .... $m/s$.

If the equation of a progressive wave is given by $y = 3 \cos \pi (100 t - x) \text{ cm}$,then what is the wavelength of the wave in $\text{cm}$?

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

The diagram shows a snapshot of a wave at time $t = 0$. The particle at $x = x_1$ is moving upward at that instant. The direction of propagation of the wave is: