Q83 / 90 · JEE Main 2021 (26 Aug Shift 2) · Physics

Two waves are simultaneously passing through a string and their equations are : $y_{1} = A_{1} \sin k (x - v t), y_{2} = A_{2} \sin k (x - v t + x_{0}) .$ Given amplitudes $A_{1} = 12 mm$ and $A_{2} = 5 mm$ , $x_{0} = 3.5 cm$ and wave number $k = 6.28 {cm}^{- 1} .$ The amplitude of resulting wave will be _____ $mm .$

Correct answer: 7

Solution

$Δ ϕ = {kx}_{0} = \frac{2 π}{λ} x_{0} = 2 π \times 3.5 (λ = \frac{2 π}{k} = 1)$

$= 2 π \times \frac{35}{10} = 7 π$

$A_{R} = \sqrt{12^{2} + 5^{2} + 2 \times 12 \times 5 \times \cos (7 π)} = \sqrt{(12 - 5)^{2}} = 7 mm$

Hence, the correct answer is 7.