Two harmonic travelling waves are described by the equations $y_1 = a \sin (kx - \omega t)$ and $y_2 = a \sin (-kx + \omega t + \phi)$. The amplitude of the superposed wave is:

State the principle of superposition of waves.

What is interference? Define its types.

Two waves are simultaneously passing through a string and their equations are:
${y}_{1} = {A}_{1} \sin {k}({x} - {vt}), {y}_{2} = {A}_{2} \sin {k}({x} - {vt} + {x}_{0}).$
Given amplitudes ${A}_{1} = 12 \, {mm}$ and ${A}_{2} = 5 \, {mm}$,${x}_{0} = 3.5 \, {cm}$,and wave number ${k} = 6.28 \, {cm}^{-1}$. The amplitude of the resulting wave will be $...... \, {mm}$.

Two waves are propagating along a taut string that coincides with the $x$-axis. The first wave has the wave function $y_1 = A \cos[k(x - vt)]$ and the second has the wave function $y_2 = A \cos[k(x + vt) + \phi]$.

There is a destructive interference between two waves of wavelength $\lambda$ coming from two different paths at a point. To get maximum sound or constructive interference at that point,the path of one wave is to be increased by