If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the waves differ in phase by

Step-by-step solution

Let the equation of two waves are y 1 = a sin ⁡ ω t - k x … i And y 2 = a sin ⁡ ω t - k x + ϕ … i i When they superpose, the resultant wave is y = y 1 + y 2 = a sin ⁡ ω t - k x + sin ⁡ ω t - k x + ϕ = a 2 sin ⁡ ω t - k x + ϕ 2 cos ⁡ - ϕ 2 = 2 a sin ⁡ ω t - k x + ϕ 2 cos ⁡ ϕ 2 = 2 a cos ⁡ ϕ 2 sin ⁡ ω t - k x + ϕ 2 … i i i Comparing Eq. (iii) with (i) or (ii), we get a = 2 a cos ⁡ ϕ 2 ⟹ cos ⁡ ϕ 2 = 1 2 ⟹ cos ⁡ ϕ 2 = cos ⁡ π 3 ∴ cos ⁡ ϕ 2 = cos ⁡ π 3 ∴ ϕ 2 = π 3 o r ϕ = 2 π 3