A string of length 25 cm and mass 2.5 g is fixed at both ends. In its first overtone it gives 8 beats s⁻¹ with a tuning fork of frequency 200 Hz. Decreasing tension decreases the beat frequency. If string tension is 3x N, find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A string of length 25 cm and mass 2.5 g is fixed at both ends. In its first overtone it gives 8 beats s⁻¹ with a tuning fork of frequency 200 Hz. Decreasing tension decreases the beat frequency. If string tension is 3x N, find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Beat frequency is |fₛ−200| = 8 Hz; possible string overtone frequencies are 192 or 208 Hz. Step 2 — Lower tension reduces fₛ; since beats decrease, fₛ is initially above 200 Hz: fₛ = 208 Hz. Step 3 — First overtone has fₛ = v/L, so v = 208 × 0.25 = 52 m s⁻¹. Step 4 — μ = 0.0025/0.25 = 0.01 kg m⁻¹ and T = μv² = 0.01 × 52² = 27.04 N. Step 5 — T ≈ 3 × 9 N; x = 9.