The equation of a wave is $Y = 6 \sin(12 \pi t - 0.02 \pi x + \frac{\pi}{3})$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is: (in $m/s$)

Waves having a velocity $10 \text{ m/s}$ strike a stationary boat near the sea shore. The distance between two consecutive crests of the waves is $40 \text{ m}$. After how many seconds do the consecutive waves strike the boat (in $\text{ s}$)?

The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative $x$-axis. Identify the correct statement$(s)$ related to the movement of the points shown in the figure. The points with maximum displacement are:

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:

$Assertion :$ Speed of wave $= \frac{\text{wavelength}}{\text{time period}}$
$Reason :$ Wavelength is the distance between two nearest particles in phase.

$A$ transverse wave is described by the equation $y = y_0 \sin 2 \pi \left( \nu t - \frac{x}{\lambda} \right)$. The maximum particle velocity is equal to four times the wave velocity if $\lambda =$