The equation of a wave is given by $y = 10 \sin \left( \frac{2 \pi}{45} t + \alpha \right)$. If the displacement is $5 \text{ cm}$ at $t = 0$,then the total phase at $t = 7.5 \text{ s}$ is

$A$ wave travelling along a string is described by the equation $y = A \sin (\omega t - k x)$. The maximum particle velocity is:

Two simple harmonic progressive waves have displacements $y_1 = a_1 \sin \left(\frac{2 \pi x}{\lambda} - \omega t\right)$ and $y_2 = a_2 \cos \left(\frac{2 \pi x}{\lambda} - \omega t + \phi\right)$. What is the phase difference between the two waves?

$A$ wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x - \frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ($y$ and $x$ are in metres and $t$ is in seconds).

$A$ particle performs $S.H.M.$ of amplitude $A$ and the wave has a wavelength $\lambda$. If $V$ is the wave velocity and $\nu$ is the maximum particle velocity,then they are related as:

The equation of a transverse wave is given by $y = 10\sin \pi (0.01x - 2t)$ where $x$ and $y$ are in $cm$ and $t$ is in seconds. Its frequency is .... $sec^{-1}$.