In the given progressive wave equation,what is the maximum velocity of the particle? $Y = 0.5 \sin(10\pi t - 5x) \text{ cm}$

$A$ longitudinal wave is represented by $x = 10 \sin 2 \pi (nt - \frac{x}{\lambda}) \, cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

If a travelling wave is given by $y(x, t) = 0.5 \sin (70.1 x - 10 \pi t)$,where $x$ and $y$ are in metre,the time $t$ is in second,then the frequency of the wave is (in $Hz$)

The equation of a progressive wave is $y = 4 \sin(4 \pi t - 0.04 x + \pi / 3)$, where $x$ is in meters and $t$ is in seconds. The velocity of the wave is:

For a wave equation $Y = Y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right) \text{ cm}$,the condition for the maximum particle velocity to be four times the wave velocity is:

The equation of a plane progressive wave is given by $y = 0.025 \sin (100t + 0.25x)$. The frequency of this wave would be