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 distance between two consecutive points with a phase difference of $60^{\circ}$ in a wave of frequency $500\,Hz$ is $6.0\,m$. The velocity with which the wave is traveling is $.........\,km/s$.

For the wave $y(x, t) = 3.0 \sin (36 t + 0.018 x + \pi / 4)$,plot the displacement $(y)$ versus time $(t)$ graphs for $x = 0, 2$ and $4 \; cm$. What are the shapes of these graphs? In which aspects does the oscillatory motion in a travelling wave differ from one point to another: amplitude,frequency,or phase?

Two waves are represented by the equations: $y_1 = a \sin(\omega t + kx + 0.57) \ m$ and $y_2 = a \cos(\omega t + kx) \ m$,where $x$ is in $meters$ and $t$ is in $seconds$. The phase difference between them is ..... $radian$.

For a wave propagating in a medium, identify the property that is independent of the others.

$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if: