Two points on a travelling wave having frequency $500\, Hz$ and velocity $300\, m/s$ are $60^{\circ}$ out of phase,then the minimum distance between the two points is ..... $m$.

$A$ transverse wave propagates in a medium with a velocity of $1450 \, m/s$. The distance between the nearest points at which the oscillations of the particles are in the opposite phase (phase difference of $\pi$) is $0.1 \, m$. What is the frequency of the wave in $Hz$?

The equation of a transverse wave is given by $y = 10\sin \pi (0.01x - 2t)$ where $x$ and $y$ are in $cm$ and $t$ is in seconds. Its frequency is .... $sec^{-1}$.

Define the angular wave number and provide its mathematical equation.

$A$ transverse wave of frequency $500 \,Hz$ and speed $100 \,m/s$ is travelling in the positive $x$-direction on a long string. At time $t=0 \,s$,the displacements at $x=0.0 \,m$ and at $x=0.25 \,m$ are $0.0 \,m$ and $0.02 \,m$,respectively. The displacement at $x=0.2 \,m$ at $t=5 \times 10^{-4} \,s$ is ............ $m$.

Two waves are represented by: $x_1 = A \sin \left(\omega t + \frac{\pi}{6}\right)$ and $x_2 = A \cos \omega t$. Then the phase difference between them is