Which of the following expressions represents a simple harmonic progressive wave?

$A$ sinusoidal progressive wave is generated in a string. Its equation is given by $y = (2 \text{ mm}) \sin(2\pi x - 100\pi t + \pi/3)$. The time when the particle at $x = 4 \text{ m}$ first passes through the mean position will be:

Which of the following statements is incorrect during the propagation of a plane progressive mechanical wave?

$A$ progressive wave of frequency $500 \,Hz$ is travelling with a velocity of $360 \,ms^{-1}$. The distance between two points, having a phase difference of $60^{\circ}$, is ............. (in $\,m$)

The equation of a plane progressive wave is given by $y = 5 \cos \pi (200t - \frac{x}{150})$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is . . . . . . m/s.

The equation of a progressive wave is $Y = a \sin 2 \pi (n t - \frac{x}{5})$. The ratio of maximum particle velocity to wave velocity is