$A$ progressive wave is represented by $y=12 \sin (5 t-4 x) \ cm$. On this wave,how far away are the two points having a phase difference of $90^{\circ}$?

The equation of a progressive wave is given by $y = 0.5 \sin(10t + x) \text{ m}$. What is the wave velocity in $\text{m/s}$?

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 $cm$?

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:

Which of the following is not true for the progressive wave $y = 4\sin 2\pi \left( \frac{t}{0.02} - \frac{x}{100} \right)$,where $y$ and $x$ are in $cm$ and $t$ is in $sec$?

$y=3 \sin \pi\left(\frac{t}{2}-\frac{x}{4}\right)$ 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 $\,m$)