Which pair of transverse waves forms a stationary wave on superposition? z₁ = a cos(kx - ωt), z₂ = a cos(kx + ωt), z₃ = a cos(ky - ωt).
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Question

Which pair of transverse waves forms a stationary wave on superposition? z₁ = a cos(kx − ωt), z₂ = a cos(kx + ωt), z₃ = a cos(ky − ωt).

G1 Physics · Accepted Answer

Step 1: Write the stationary wave as y = 2A sin(kx) cos(ωt + φ) or 2A cos(kx) sin(ωt + φ). Step 2: Nodes satisfy the spatial factor = 0 and adjacent nodes are λ/2 apart; antinodes lie midway. Step 3: Apply the boundary conditions and harmonic number. Final: A: A and B.