Equation of motion in the same direction is given by ${y_1} = A\sin (\omega t - kx)$, ${y_2} = A\sin (\omega t - kx - \theta )$. The amplitude of the medium particle will be
Medium
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(a)The resultant amplitude is given by
${A_R} = \sqrt {{A^2} + {A^2} + 2AA\cos \theta } = \sqrt {2{A^2}(1 + \cos \theta )} $
$ = 2A\cos \theta /2$
${A_R} = \sqrt {{A^2} + {A^2} + 2AA\cos \theta } = \sqrt {2{A^2}(1 + \cos \theta )} $
$ = 2A\cos \theta /2$
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