Explain the amplitude and phase of a wave.

(N/A) The magnitude of the maximum displacement of a particle participating in the propagation of a wave is called the amplitude of the wave. It is represented by the symbol $a$ or $A$.
According to the wave equation:
$y = a \sin(kx - \omega t + \phi)$
Since the value of $\sin(kx - \omega t + \phi)$ has extreme values $\pm 1$,we can write:
$y_{\max} = a(\pm 1) = \pm a$
Therefore,the amplitude of the wave is $|y_{\max}| = a$.
The amplitude of a wave is always positive. Its $SI$ unit is $m$ and its dimensional formula is $[M^0 L^1 T^0]$.
Initial phase $(\phi)$: If we know the initial position of a particle at the origin of the wave and the direction of its motion at time $t = 0$,we can find the value of the initial phase $\phi$ using:
$y(x, t) = a \sin(\omega t - kx + \phi)$
Putting $x = 0$ and $t = 0$,we get $y(0, 0) = a \sin \phi$.
By knowing $\sin \phi$,we can determine the initial phase $\phi$.
In the wave equation $y = y(x, t) = a \sin(\omega t - kx + \phi)$,the argument of the sine function $(\omega t - kx + \phi)$ is called the total phase of the wave at time $t$ at a distance $x$ from its source. It represents the total phase of oscillation of a particle at distance $x$ from the origin of the wave at time $t$.