Equations of motion in the same direction are given by aligned & y₁=2 a ( t-k x) & y₂=2 a ( t-k x- ) aligned The amplitude of the medium particle will be

Step-by-step solution

The given equations of motion are aligned & y₁=2 a ( t-k x) & y₂=2 a ( t-k x- ) aligned Now the resultant equation of wave is given by aligned & y=y₁+y₂ & =2 a ( t-k x)+2 a ( t-k x- ) & y=2 a [2 ( t-k x+ t-k x- ) 2 t-k x-( t-k x- ) 2 ] aligned y=4 a 2 ( t-k x- 2 ) ...(1) Now comparing equation (1) with y=A ( t-k x) , we have Resultant amplitude A=4 a 2