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

The equation of a progressive wave is given by $y = A \cos 240(t - x/12)$,where $t$ is the time in seconds and $x$ is the distance in meters. The phase difference (in radians) between two positions $0.5 \, m$ apart is:

The equation of a progressive wave is given by $y = a \sin \pi (40t - x)$,where $a$ and $x$ are in meters and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

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

Write the definition of the speed of a progressive wave and derive $v = \frac{\omega}{k}$ and $v = \frac{\lambda}{T}$.

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.