In a resonance-column experiment, successive resonance lengths are ℓ₁=30.7 cm and ℓ₂=63.2 cm for a 512 Hz fork. Using v=fλ and λ=2(ℓ₂-ℓ₁), find the maximum error in v.
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Question

In a resonance-column experiment, successive resonance lengths are ℓ₁=30.7 cm and ℓ₂=63.2 cm for a 512 Hz fork. Using v=fλ and λ=2(ℓ₂−ℓ₁), find the maximum error in v.

G1 Physics · Accepted Answer

λ=2(63.2−30.7)=65.0 cm. With readings to 0.1 cm, each length has maximum error ±0.05 cm, so Δλ=2(0.05+0.05)=0.20 cm. Thus Δv=fΔλ=512×0.20=102.4 cm s⁻¹. Correct answer: D.