$A$ 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?

For a wave equation $y = 8 \sin 2\pi (0.1x - 2t) \, cm$,find the phase difference in $^\circ$ between two particles separated by a distance of $2 \, cm$.

$A$ travelling wave is described by the equation $y(x, t) = 0.05 \sin(8x - 4t) \; m$. The velocity of the wave is $..... \; m/s$ [all the quantities are in $SI$ units].

The equation of a wave travelling on a string is $y = \sin(20 \pi x + 10 \pi t)$,where $x$ and $t$ are distance and time in $SI$ units. The minimum distance between two points having the same oscillating speed is (in $cm$)

The figure given shows a sinusoidal wave on a string. If the frequency of the wave is $150 \, Hz$,what is the wavelength and velocity of the given wave?

$A$ wave is propagating along the $x$-axis. The displacement of particles of the medium in the $z$-direction at $t = 0$ is given by: $z = \exp[-(x + 2)^2]$,where $x$ is in meters. At $t = 1 \ s$,the same wave disturbance is given by: $z = \exp[-(2 - x)^2]$. Then,the wave propagation velocity is: