Two waves y₁ = A₁ sin k(x − vt) and y₂ = A₂ sin k(x − vt + x₀) travel together. Given A₁ = 12 mm, A₂ = 5 mm, x₀ = 3.5 cm and k = 6.28 cm⁻¹, find the resultant amplitude in mm.
Physics · Wave Motion
JEE Mains 2021

Question

Two waves y₁ = A₁ sin k(x − vt) and y₂ = A₂ sin k(x − vt + x₀) travel together. Given A₁ = 12 mm, A₂ = 5 mm, x₀ = 3.5 cm and k = 6.28 cm⁻¹, find the resultant amplitude in mm.

G1 Physics · Accepted Answer

Step 1: Phase difference = kx₀ = 6.28×3.5 ≈ 21.98 rad ≈ 7π, so the two waves are nearly opposite in phase. Step 2: Resultant amplitude = |A₁−A₂| = |12−5| = 7 mm. Final answer: 7.