Equation of motion in the same direction are given by
${y_1} = 2a\sin (\omega t - kx)$ and ${y_2} = 2a\sin (\omega t - kx - \theta )$
The amplitude of the medium particle will be
Medium
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(c)Resultant amplitude
${A_R} = 2A\cos \,\left( {\frac{\theta }{2}} \right) = 2 \times (2a)\cos \,\left( {\frac{\theta }{2}} \right) = 4a\cos \,\left( {\frac{\theta }{2}} \right)$
${A_R} = 2A\cos \,\left( {\frac{\theta }{2}} \right) = 2 \times (2a)\cos \,\left( {\frac{\theta }{2}} \right) = 4a\cos \,\left( {\frac{\theta }{2}} \right)$
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