Four strings have linear densities μ, 2μ, 3μ and 4μ. Their lengths are L₀, 3L₀/2, 5L₀/4 and 7L₀/4, and they vibrate in the 1st, 3rd, 5th and 14th harmonics at the same frequency. Tension values are to be matched with List-II in units of T₀. Which option gives the correct matching?

Question

G1 Physics · Accepted Answer

Step 1: For a stretched string, v = √(T/μ) and fₙ = nv/(2L) for fixed ends. Step 2: Use the stated node/antinode or harmonic condition; for composite wires the same frequency must hold on both parts. Step 3: Solve with the given lengths, densities and tension. Final: A: I → P, II → Q, III → T, IV → U.