$A$ progressive wave of frequency $50 \,Hz$ is travelling with velocity $350 \,m/s$ through a medium. The change in phase at a given time interval of $0.01 \,s$ 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 $Y = 3 \sin \left[ \pi \left( \frac{t}{3} - \frac{x}{5} \right) + \frac{\pi}{4} \right]$ where $X$ and $Y$ are in metre and time in second. Which of the following is correct?

The equation of a progressive wave is given by $y = a \sin(628t - 31.4x)$. If the distances are expressed in $cm$ and time in seconds,then the wave velocity will be ...... $cm/sec$.

The equation of a progressive wave is $y = 0.2 \sin 2\pi \left[ \frac{t}{0.01} - \frac{x}{0.3} \right]$,where $x$ and $y$ are in meters and $t$ is in seconds. The velocity of propagation of the wave is .... $m/s$.

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 $cm$?