$A$ transverse wave is represented by $y = A \sin(\omega t - kx)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

The equation of a progressive wave is given by $x = 0.05 \cos \left( 4\pi t + \frac{\pi}{4} \right) \, m$. What is the frequency of the wave in $Hz$?

In a medium, the phase difference between two particles separated by a distance $x$ is $\frac{\pi}{5} \text{ rad}$. If the frequency of the oscillation of particles is $25 \text{ Hz}$ and the velocity of propagation of the wave is $75 \text{ m/s}$, then the value of $x$ is (in $\text{ m}$)

$A$ transverse wave in a medium is described by the equation $y = A \sin^2 (\omega t - kx)$. The magnitude of the maximum velocity of particles in the medium will be equal to that of the wave velocity,if the value of $A$ is ($\lambda$ = wavelength of wave).

$A$ transverse wave on a string is described by $y = 3 \sin(36t + 0.018x + \pi/4)$, where $x$ and $y$ are in $cm$ and $t$ is in seconds. The least distance between two successive crests in the wave is . . . . . . $cm$. (Nearest integer) $(\pi = 3.14)$

The wave described by $y = 0.25 \sin(10\pi x - 2\pi t)$,where $x$ and $y$ are in $meters$ and $t$ in $seconds$,is a wave travelling along: