250+ TOP MCQs on Principle of Superposition of Waves | Class 11 Physics

Physics Multiple Choice Questions on “Principle of Superposition of Waves”.

1. y₁ = 2sin(3x – 2t) & y₂ = 3sin(3x – 2t + π/4). Find the expression for resultant displacement caused by superposition of the two waves.
a) 3.6sin(2x-3t+3π/7)
b) 4.63sin(3x-2t+3π/5)
c) 3.6cos(3x-2t+3π/7)
d) 4.63cos(3x-2t+3π/5)
Answer: b
Clarification: y = y₁ + y₂= 2sin(3x-2t) + 3sin(3x-2t+π/4)
= Asin(3x-2t+φ).
A² = A₁² + A₂² + 2A₁A₂cosθ, where θ = π/4, A₁ = 2 & A₂ = 3.
∴ A = sqrt(4+9+12/√2) = 4.63m.
Tanφ = A₂sinθ / (A₁ + A₂cosθ)
= (3/√2)/(2+3/√2) = 0.51. ∴ φ = 27rad.
∴ y = 4.63sin(3x-2t+8.6π) = 4.63sin(3x-2t+3π/5).

2. A wave having an amplitude of 3cm is to be superimposed with another wave of the same amplitude. What should be their phase difference if the net amplitude has to be 0?
a) π/2
b) π
c) 2π
d) 0
Answer: b
Clarification: The net amplitude is given by: A² = A₁² + A₂² + 2A₁A₂cosθ,
where θ is the phase difference.
For A to be zero 9 + 9 + 2(9)(9)cosθ = 0
∴ θ = π.

3. If the two pulses of equal amplitude have 2J of energy each, what will be the energy of the system when they overlap with each other making the string entirely straight?

a) 0
b) 4J
c) 2J
d) 1J
Answer: b
Clarification: When the two pulses overlap, the string will become straight and the total energy will be in the form of kinetic energy.
As energy will be conserved, energy at that instant = 2+2 = 4J.

4. In superposition of waves the displacements get added like vectors. True or False?
a) True
b) False
Answer: a
Clarification: When waves interfere, the resultant displacement is given by vector addition of their individual displacements.