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Question

A piano wire A vibrates at a fundamental frequency of 600 Hz. A second identical wire B produces 6 beats per second with it when the tension in A is slightly increased. Find the the ratio of the tension in A to the tension in B.

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Solution

Mass per unit length of both the wires​ = m

Fundamental frequency of wire of length l and tension T is given by:

n=12ITm

It is clear from the above relation that as the tension increases, the frequency increases.

Fundamental frequency of wire A is given by:

nA=12ITAm

Fundamental frequency of wire B is given by:

nB=12ITBm

It is given that 6 beats are produced when the tension in A is increased.

⇒​ nA=606=12lTAm
Therefore, the ratio can be obtained as:

nAnB=606600=1/2ITA/m1/2ITB/m606600=TATB TATB=606600=1.01 TATB=1.02

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