$A$ sound of frequency $480 \,Hz$ is emitted from a stringed instrument. The velocity of sound in air is $320 \,m/s$. After completing $180$ vibrations, the distance covered by the wave is: (in $\,m$)

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents a

How is the motion of a point having a constant phase measured?

$A$ wave of frequency $500 \, Hz$ has a velocity of $360 \, m/s$. The distance between two nearest points $60^o$ out of phase is .... $cm$.

$A$ transverse wave on a string is described by $y = 3 \sin(36t + 0.018x + \pi/4)$, where $x$ and $y$ are in $cm$ and $t$ is in seconds. The least distance between two successive crests in the wave is . . . . . . $cm$. (Nearest integer) $(\pi = 3.14)$

If the speed of the wave shown in the figure is $330 \ m/s$ in the given medium,then the equation of the wave propagating in the positive $x$-direction will be (all quantities are in $M.K.S.$ units).