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Question:

Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both the wires oscillate together would be?

0.02

0.01

0.03

0.04

Solution:

Frequency ν=v/2L where v=√(T/μ) ⇒ ν=(1/2L)√(T/μ)
Thus fractional change in frequency Δν/ν = (1/2)ΔT/T
Given : Δν=6, ν=600 Hz
∴ 6/600 = (1/2)ΔT/T
⇒ ΔT/T = 2 × 0.01 = 0.02