Explain about amplitude and phase of wave.

Explanation

"Magnitude of maximum displacemetn of a particle taking part in the propagation of wave is called amplitude of wave." It is shown by symbol a or A.
According to wave equation,
`y=a sin (kx - omega t + phi)`
Now since the vaue of`sin (omega t - kx + phi)` has exteme values `pm 1` we can write:
`y _(max) =a (pm1) =pma`
`therefore` Amplitude of wave `= |y_(max)| =a`
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 wave and direction of its motion on its path a time `t=0,` then we can find out value of initial phase `phi` using,
`y (x,t) =a sin (omega t - kx + phi)`
Putting `x =0 and t =0, y (0,0) =a in phi`
Here knowing `sin phi, ` we can find out initial phase `phi.`
In the wave equation ,
`y=y (x,t) =a sin (omega t - kx + phi)` th argument of sine function is `(omega t - kx + phi)` Which is called total phase of a wave at time t at a distance x from its source. It also gives total phase of oscillation of a particle at distance x from origin of wave at time t.