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

$A$ progressive wave moving along the $x$-axis is represented by $y = A \sin \left[ \frac{2 \pi}{\lambda} (vt - x) \right]$. The wavelength $\lambda$ at which the maximum particle velocity is $3$ times the wave velocity is:

The equation of a progressive wave is $Y = 3 \sin \left[ \pi \left( \frac{t}{3} - \frac{x}{5} \right) + \frac{\pi}{4} \right]$ where $x$ and $y$ are in meters and time $t$ is in seconds. Which of the following is correct?

The equation of a progressive wave is given by $y = 0.2 \cos \pi (0.04t + 0.02x - \frac{\pi}{6})$. The distance is expressed in $cm$ and time in seconds. What will be the minimum distance between two particles having a phase difference of $\pi / 2$ in $cm$?

$A$ wave is represented by $x = 0.4 \cos \left(8t - \frac{y}{2}\right)$ where $x$ and $y$ are in meters and $t$ is in seconds. The speed of the wave is