If two waves y₁ = A ( t - 0.1x) and y₂ = A ( t - 0.1x - 2 ) are superimposed on each other, then the resultant amplitude due to superposition of waves is

Step-by-step solution

The given waves are y₁ = A ( t - 0.1x) and y₂ = A ( t - 0.1x - 2 ) . The phase difference between the two waves is = 2 . The resultant amplitude A_R of two superimposed waves is given by: A_R = A₁^2 + A₂^2 + 2A₁A₂ ( ) Substituting A₁ = A , A₂ = A , and = 2 : A_R = A^2 + A^2 + 2A^2 ( 2 ) A_R = 2A^2 (1 + 2 ) Using the trigonometric identity 1 + = 2 ^2 ( 2 ) : A_R = 2A^2 (2 ^2 4 ) A_R = 4A^2 ^2 4 A_R = 2A 4 Answer: 2A 4