Given noticeable points, about the amplitude of resultant waves of two harmonic progressive waves on stretached string.

Explanation

The amplitude of resultant wave is a function of phase difference `phi` between two element waves.
`A (phi) =2 a cos "" (phi)/(2)`
When two waves have same phase, then `phi =0 ` hence,` y (x,t) =2a sin (kx - omega t )`
Relultant amplitude is `A = 2a. `It is maximum amplitude.
If `phi =pi` the two waves are completely out of phase, the amplitude of the resultant wave reduces to zero.
`therefore (x ,t)= 0 [because A (phi) = 2 cos "" (phi)/(2) = 2 a cos "" (pi)/(2) =0]`