The equation of a progressive wave is given by $y = a \sin \pi [\frac{t}{2} - \frac{x}{4}]$,where $t$ is in seconds and $x$ is in meters. The distance through which the wave moves in $8 \ s$ is .... $(m)$

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 $Y = 3 \sin \left[ \pi \left( \frac{t}{3} - \frac{x}{5} \right) + \frac{\pi}{4} \right]$ where $X$ and $Y$ are in metre and time in second. Which of the following is correct?

Among the following,the equation representing a progressive wave is
$(A)$ $y=2 \cos 3x \sin 10t$
$(B)$ $y=2 \sqrt{x-vt}$
$(C)$ $y=3 \sin (5x-0.5t)+4 \cos (5x-0.5t)$
$(D)$ $y=\cos x \sin t+\cos 2x \sin 2t$

The equation of a plane progressive wave is given by $y = 0.6 \sin 2\pi (t - x/2)$. On reflection from a denser medium,its amplitude becomes $2/3$ of the amplitude of the incident wave. The equation of the reflected wave is:

$y=3 \sin \pi\left(\frac{t}{2}-\frac{x}{4}\right)$ represents an equation of a progressive wave,where $t$ is in $s$ and $x$ is in $m$. The distance travelled by the wave in $5 \,s$ is (in $\,m$)