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

$A$ plane progressive wave is given by $y = 2 \cos 2 \pi (330 t - x) \ m$. The frequency of the wave is: (in $Hz$)

The rope shown at an instant is carrying a wave travelling towards the right,created by a source vibrating at a frequency $n$. Consider the following statements:
$I.$ The speed of the wave is $4n \times ab$
$II.$ The medium at $a$ will be in the same phase as $d$ after $\frac{4}{3n} \text{ s}$
$III.$ The phase difference between $b$ and $e$ is $\frac{3\pi}{2}$
Which of these statements are correct?

Give the definition,$SI$ unit,and dimensional formula of the time period,angular frequency,and frequency of a wave.

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 $.........\,km/s$.

Two waves of frequencies $20 Hz$ and $30 Hz$ travel out from a common point. The phase difference between them after $0.6 s$ is: