Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
Two waves having an equal amplitude A and the same frequency propagate in the same direction within a medium. The amplitude of the resultant wave is
Options
- AA
- Bbetween 0 and 2A
- C0
- D2A
Correct answer
B. between 0 and 2A
Step-by-step solution
Let the two waves be y₁ = A ( t - kx) and y₂ = A ( t - kx + ) . By the principle of superposition, the amplitude of the resultant wave is given by A_R = A₁^2 + A₂^2 + 2A₁A₂ . Substituting A₁ = A₂ = A , we get A_R = A^2 + A^2 + 2A^2 = 2A^2(1+ ) . Using the trigonometric identity 1+ = 2 ^2 ( 2 ) , we get A_R = 2A | ( 2 ) | . Since the phase difference is not specified, it can take any value. The maximum amplitude occurs when ( 2 ) = 1 , giving A_ max = 2A . The minimum amplitude occurs when ( 2 ) = 0 , giving A_ min