What are called progressive waves? What is called a wave equation? Write the wave equation for a progressive harmonic transverse wave propagating and explain it by drawing graphs.

(N/A) $1$. Progressive Wave: $A$ wave that travels continuously in a medium in a specific direction without any change in its form is called a progressive or traveling wave.
$2$. Wave Equation: $A$ mathematical expression that describes the displacement of particles of the medium as a function of both position $(x)$ and time $(t)$ is called a wave equation.
$3$. Wave Equation for a Progressive Harmonic Transverse Wave: The displacement $y$ of a particle at position $x$ and time $t$ is given by $y(x, t) = A \sin(kx - \omega t + \phi)$,where $A$ is the amplitude,$k = \frac{2\pi}{\lambda}$ is the angular wave number,$\omega = 2\pi f$ is the angular frequency,and $\phi$ is the initial phase constant.
$4$. Graphical Explanation:
- $y-x$ graph (at constant $t$): Represents the snapshot of the wave at a specific instant,showing the spatial variation of displacement.
- $y-t$ graph (at constant $x$): Represents the oscillation of a single particle at a fixed position over time.