A sonometer wire of length 10 cm and mass 1 g is under tension 64 N and resonates in its fundamental mode with a tuning fork. The fork is then moved away from the wire; a nearby observer hears 1 beat s⁻¹. The fork speed is v/4 m s⁻¹. If sound speed is 300 m s⁻¹, find v.
Physics · Wave Motion
JEE Mains Practice

Question

A sonometer wire of length 10 cm and mass 1 g is under tension 64 N and resonates in its fundamental mode with a tuning fork. The fork is then moved away from the wire; a nearby observer hears 1 beat s⁻¹. The fork speed is v/4 m s⁻¹. If sound speed is 300 m s⁻¹, find v.

Physics · Wave Motion

G1 Physics · Accepted Answer

Step 1: The wire has μ = m/L = 0.001/0.10 = 0.01 kg m⁻¹. Its wave speed is √(T/μ) = √(64/0.01) = 80 m s⁻¹, so the fundamental frequency is 80/(2×0.10) = 400 Hz. Step 2: If the fork moves away at speed u, the nearby stationary observer hears f′ = 400×300/(300+u). One beat per second means 400−f′ = 1. Solving gives u ≈ 0.75 m s⁻¹. Step 3: Given u = v/4, v ≈ 3. Final answer: 3.