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, .....) :

Question

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, .....) : (A) v = (n/2)√(T/ML) (B) v = (n/2L)√(T/M) (C) v = (1/2n)√(T/ML) (D) v = (n/2)√(TL/M)

Tardigrade Admin · Accepted Answer

v = (n/2L)√(T/μ) = (n/2)√(T/ML)

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 $n = 1, 2, 3, .....$ ) :

$v = \frac{n}{2} \frac{T}{M L}$

$v = \frac{n}{2 L} \frac{T}{M}$

$v = \frac{1}{2 n} \frac{T}{M L}$

$v = \frac{n}{2} \frac{T L}{M}$

$v = \frac{n}{2 L} \frac{T}{μ} = \frac{n}{2} \frac{T}{M L}$

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,.....) :

v=2n​MLT​​

v=2Ln​MT​​

v=2n1​MLT​​

v=2n​MTL​​