Explain linearly polarized waves and provide their definition.

(N/A) Consider a long string held horizontally with one end fixed. If we move the free end of the string up and down in a periodic manner,a wave is generated propagating in the $+x$-direction as shown in figure $(a)$.
The curves represent the displacement of the string at $t=0$ and at $t=\Delta t$ respectively as the sinusoidal wave propagates in the $+x$-direction.
In figure $(b)$,the curve represents the time variation of the displacement at $x=0$ for the same wave.
The displacement of the wave in the $+x$-direction occurs in the $y$-direction,so its equation is given by:
$y(x, t) = a \sin(kx - \omega t)$
where $a$ is the amplitude of the wave,$\omega = 2\pi\nu$ is the angular frequency,and $k = \frac{2\pi}{\lambda}$ is the wave vector.
According to this equation,the displacement of the string particles (in the $y$-direction) is at right angles to the direction of propagation of the wave,making it a transverse wave. Since the displacement is restricted to the $y$-direction,it is called a $y$-polarized wave.
Definition: $A$ wave is called linearly polarized if the displacement of the particles of the medium is confined to a single straight line perpendicular to the direction of wave propagation. Since each point on the string moves along a straight line,this is a linearly polarized wave. Because the string remains confined to the $xy$-plane,it is also called a plane-polarized wave.