Question

Giving reason for you selection, select pairs out of the following four waves in a medium which will give rise to (i) beats, (ii) destructive interference, (iii) stationary waves.

(i) ξ₁ = Acos 2π(v₁t + \(\frac{x}{\lambda_1}\) )

(ii) ξ₂ = Acos 2π(v₁t + \(\frac{x}{\lambda_1}+\pi\) )

(iii) ξ₃ = Acos 2π(v₁t + \(\frac{x}{\lambda_2}\) )

(iv) ξ₄ = Acos 2π(v₁t − \(\frac{x}{\lambda_2}\) )

Answer 1

(i) The pairs (1) and (3) will give rise to beats as they represent two simple harmonic waves of slightly different frequency. Travelling in the same direction.

(ii) The pairs (1) and (2) will produce destructive interference as they represent two identical waves with a phase difference of π, travelling in the same direction.

(iii) The pairs (3) and (4) represent identical waves travelling in opposite directions. They will give rise to stationary waves.