For waves propagating in a medium,identify the property that is independent of the others.

Explain linearly polarized waves and provide their definition.

If the wavelength of a wave is $\lambda = 6000 \mathring{A}$,then the wave number will be:

$A$ wave is given by $Y = 3 \sin 2 \pi \left( \frac{t}{0.04} - \frac{x}{0.01} \right)$ where $Y$ is in $cm$. The frequency of the wave and the maximum acceleration will be $(\pi^2 = 10)$.

State whether the following statements are True or False:
$(i)$ In the case of propagation of longitudinal waves,the angle between the directions of particle velocity and wave velocity is $0^{\circ}$ or $180^{\circ}$.
$(ii)$ In the case of propagation of transverse waves,the angle between the directions of particle velocity and wave velocity is $\pi \text{ rad}$.
$(iii)$ Along the direction of propagation of a wave,the distance between two particles having the same phase is called the wavelength of the wave.
$(iv)$ When a wave is reflected from a rarer medium,its phase increases by an amount of $\pi \text{ rad}$.

$A$ 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 ............ $m$.