The equation of a wave is given by $Y = 10^{-2} \sin 2 \pi (160 t - 0.5 x + \frac{\pi}{4})$,where $x$ and $Y$ are in $m$ and $t$ is in $s$. The speed of the wave is $..... \, km \, h^{-1}$.

Write the equation of the relation between wave speed $(v)$,angular frequency $(\omega)$,and angular wave number $(k)$.

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

$A$ sinusoidal wave of wavelength $7.5 \ cm$ travels a distance of $1.2 \ cm$ along the $x$-direction in $0.3 \ s$. The crest $P$ is at $x = 0$ at $t = 0 \ s$ and the maximum displacement of the wave is $2 \ cm$. Which equation correctly represents this wave?

The wave equation is $y = 0.30 \sin (314t - 1.57x)$ where $t, x$ and $y$ are in second,meter and centimeter respectively. The speed of the wave is ..... $m/s$.

$A$ wave travelling along the $x$-axis is described by the equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and the time period of the wave are $0.08 \ m$ and $2.0 \ s$ respectively,then $\alpha$ and $\beta$ in appropriate units are: