For a wave represented by the equation $y = 3 \cos \left( \frac{x}{4} - 10t - \frac{\pi}{2} \right)$,what is the maximum velocity of the particle of the medium?

The equation of a wave is given by $Y = 7 \sin(7\pi t - 0.04\pi x + \frac{\pi}{3})$. What is the wave speed in $m/s$?

$A$ plane wave $y = A \sin \omega \left( t - \frac{x}{v} \right)$ undergoes normal incidence on a plane boundary separating medium $M_1$ and $M_2$ and splits into a reflected and transmitted wave having speeds $v_1$ and $v_2$. Then:

The displacement of a wave travelling in the $x$ direction is $y = 10^{-4} \sin(600t - 2x + \pi/3) \text{ m}$,where $x$ is in metres and $t$ is in seconds. The speed of the wave is: (in $\text{ m/s}$)

$A$ 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 .....................

The speed of a wave in a medium is $960 \, m/s$. If $3600$ waves pass through a point in the medium in $1 \, minute$,what is the wavelength of the wave in $meters$?