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

What is the phase difference between two particles $25 \ m$ apart in a wave represented by the equation $y=0.03 \sin (\pi[2 t-0.01 x])$ traveling in a medium?

The equation of a wave traveling along the $x$-axis is given by $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and time period of the wave are $0.08 \ m$ and $2.0 \ s$ respectively,find the values of $\alpha$ and $\beta$ in appropriate units.

In the wave equation $y = 0.5 \sin \frac{2 \pi}{\lambda}(400 t - x ) \, m$,the velocity of the wave will be ......... $m/s$.

The equation of a plane progressive wave is given by $y = 0.025 \sin (100t + 0.25x)$. The frequency of this wave would be

An observer standing near the sea shore observes $54$ waves per minute. If the wavelength of the water wave is $10 \ m$,then the velocity of the water wave is .... $m/s$.