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A piano wire A vibrates at a fundamental...

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 ratio of the tension in A to the tension in B.

Text Solution

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The correct Answer is:
A, B
Here given `n_B=1/(2I) sqrt(T_B/M)`
As the tension increases frequency increases.
It is given that 6 beats are produced when tension in A is increased
So, `n_A=606=/(2I) sqrt(T_A/M)`
`rarr n_A/n_B=600/606`
`=((1/(2I))sqrt((T_B/M))/((I/(2I)sqrt((T_A/M))`
`=sqrtT_B/sqrtT_A`
`rarr sqrtT_A/sqrtT_B=606/600=1.01`
` T_A/T_B=1.02`
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