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Question: Answered & Verified by Expert
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 $n=1,2,3, \ldots)$
PhysicsWaves and SoundJEE Main
Options:
  • A $v=\frac{n}{2} \sqrt{\frac{T}{M L}}$
  • B $v=\frac{n}{2 L} \sqrt{\frac{T}{M}}$
  • C $v=\frac{1}{2 n} \sqrt{\frac{T}{M L}}$
  • D $v=\frac{n}{2} \sqrt{\frac{T L}{M}}$
Solution:
2874 Upvotes Verified Answer
The correct answer is: $v=\frac{n}{2} \sqrt{\frac{T}{M L}}$
The formula of frequency of 3 vibrations produced in tensed wire is
$$
v=\frac{n}{2} \sqrt{\frac{T}{m}}
$$
$m=$ Mass per unit length of the wire $=\frac{M}{L}$
$M=$ Mass of wire
$L=$ Length of wire $n=$ Number of loops produced in wire $v=\frac{n}{2 L} \sqrt{\frac{T}{M / L}}=\frac{n}{2} \sqrt{\frac{T}{M L}}$

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