A wave represented by the equation y = A cos (kx - ωt) is superimposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation of the other wave is:
Options

Question

A wave represented by the equation y = A cos (kx − ωt) is superimposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation of the other wave is:

G1 Physics · Accepted Answer

Step 1: Add the waves as phasors. For two amplitudes A₁,A₂ with phase difference φ, A² = A₁² + A₂² + 2A₁A₂ cosφ. Step 2: Intensity is proportional to A²; constructive/destructive conditions are Δ = nλ and Δ = (n+½)λ. Step 3: Apply the stated phases/path differences. Final: B: − A cos (kx + ωt).