$A$ body sends a wave $150 \text{ mm}$ long through medium $P$ and $0.30 \text{ m}$ long in medium $Q$. If velocity of the wave in medium $P$ is $80 \text{ cm s}^{-1}$, the velocity of wave in medium $Q$ is (in $\text{ m s}^{-1}$)

$A$ wave is represented by the equation $y = 7 \sin(7\pi t - 0.04\pi x + \frac{\pi}{3})$,where $x$ is in metres and $t$ is in seconds. The speed of the wave is:

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

The equation of a simple harmonic wave is given as $y = 5 \sin \frac{\pi}{2}(100t - x)$,where $x$ and $y$ are in meters and time $t$ is in seconds. The period of the wave is: (in $s$)

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 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.