$A$ particle on the trough of a wave at any instant will come to the mean position after a time ($T =$ time period).

The path difference between two waves $Y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$ and $Y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \phi\right)$ is

The phase difference between two waves represented by $y_1 = 10^{-6} \sin [100t + (x/50) + 0.5] \, m$ and $y_2 = 10^{-6} \cos [100t + (x/50)] \, m$,where $x$ is expressed in meters and $t$ is expressed in seconds,is approximately .... $rad$.

The equation of a wave motion (with $t$ in seconds and $x$ in metres) is given by $y = 7\sin(7\pi t - 0.4\pi x + \frac{\pi}{3})$. The velocity of the wave will be

$A$ wave of frequency $500 \, Hz$ has a velocity of $360 \, m/s$. The distance between two nearest points $60^o$ out of phase is .... $cm$.

$A$ sound wave of frequency $500 \text{ Hz}$ travels between two points $X$ and $Y$ separated by a distance of $600 \text{ m}$ in a time of $2 \text{ s}$. The number of waves between the points $X$ and $Y$ are