Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

The resultant wave formed by the superposition of two waves given by y = a ( t - kx) and y = a ( t - kx) has an amplitude of

Options

A2 , a
B0
C2a
Da

Correct answer

A. 2 , a

Step-by-step solution

The given equations of the waves are y₁ = a ( t - kx) and y₂ = a ( t - kx) . The second wave can be written as y₂ = a ( t - kx + 2 ) . The phase difference between the two waves is = 2 . The amplitude of the resultant wave is given by A = a₁^2 + a₂^2 + 2a₁ a₂ ( ) . Substituting a₁ = a , a₂ = a , and = 2 : A = a^2 + a^2 + 2a^2 ( 2 ) A = 2a^2 = 2 a .

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