A string, fixed at both ends, vibrates in a resonant mode with a separation of 2.0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. Find the length of the string.
Physics · Wave Motion
JEE Mains Advanced

Question

A string, fixed at both ends, vibrates in a resonant mode with a separation of 2.0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. Find the length of the string.

Physics · Wave Motion

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: 8.