When a wave travels in a medium,the particle displacement is given by $y = a \sin(2 \pi (bt - cx))$,where $a, b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

Write the definition of the angular frequency of a wave and its $SI$ unit.

$A$ progressive sound wave is represented by $y = a \sin(400\pi t - \pi x / 6.85)$,where $x$ is in $m$ and $t$ is in $s$. The frequency of the wave is .... $Hz$.

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 $..... \, km \, h^{-1}$.

$A$ person is producing a wave in a string by moving his hand first up and then down. If the frequency is $\frac{1}{8} \, Hz$,then find out the time taken by a particle which is at a distance of $9 \, m$ from the source to move to the lower extreme for the first time in seconds. (Given $\lambda = 24 \, m$)

$A$ wave equation is $y = 10^{-4} \sin(60t + 2x)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. Which of the following statements is correct?