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  4. A uniform string of length L and mass M is fixed at both ends while it is subject to a tension T. It can vibrate at frequencies (v) given by the formula (where n = 1, 2, 3, .....) :

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Q. A uniform string of length $L$ and mass $M$ is fixed at both ends while it is subject to a tension $T$. It can vibrate at frequencies $(v)$ given by the formula (where $n = 1, 2, 3, .....$) :

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Solution:

$v = \frac{n}{2L}\sqrt{\frac{T}{\mu}} = \frac{n}{2}\sqrt{\frac{T}{ML}}$