The equation of a plane progressive wave is given by $y = 0.6 \sin 2\pi \left( t - \frac{x}{2} \right)$. 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:

During the propagation of a plane progressive mechanical wave,which of the following statements is incorrect?

$A$ 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 given by $y = 4 \sin \left( \pi \left( \frac{t}{5} - \frac{x}{9} \right) + \frac{\pi}{6} \right)$. Which of the following is correct?

The equation of a plane progressive wave is given by $y = 5 \cos \pi (200t - \frac{x}{150})$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is . . . . . . m/s.

$A$ transverse harmonic wave on a string is described by $y(x, t) = 3.0 \sin (36t + 0.018x + \pi/4)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The positive direction of $x$ is from left to right.
$(a)$ Is this a travelling wave or a stationary wave? If it is travelling,what are the speed and direction of its propagation?
$(b)$ What are its amplitude and frequency?
$(c)$ What is the initial phase at the origin?
$(d)$ What is the least distance between two successive crests in the wave?