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

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

Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent a travelling wave.

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

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 $sec$?

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: