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 $m/s$)

The equation of a progressive wave is $y = 8 \sin \left[ \pi \left( \frac{t}{10} - \frac{x}{4} \right) + \frac{\pi}{3} \right]$. The wavelength of the wave is .... $m$.

The phase difference between two points separated by $1 \ m$ in a wave of frequency $120 \ Hz$ is $90^o$. The wave velocity is .... $m/s$.

$A$ travelling acoustic wave of frequency $500 Hz$ is moving along the positive $x$-direction with a velocity of $300 ms^{-1}$. The phase difference between two points $x_{1}$ and $x_{2}$ is $60^{\circ}$. The minimum separation between the two points is:

The figure represents the instantaneous snapshot of a transverse harmonic wave traveling along the negative $x$-axis. Identify the correct point(s) moving in the negative $y$-direction (downward).

$A$ plane progressive wave is represented by the equation $y = 0.1 \sin \left( 200\pi t - \frac{20\pi x}{17} \right)$,where $y$ is displacement in $m$,$t$ is in seconds,and $x$ is the distance from a fixed origin in meters. The frequency,wavelength,and speed of the wave respectively are: