When a stretched wire of fundamental frequenc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The fundamental frequency of a stretched wire is given by $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $L$ is the length,$T$ is the tension,and $

Vedclass · Accepted Answer

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$

Vedclass · Answer

(C) The fundamental frequency of a stretched wire is given by $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $L$ is the length,$T$ is the tension,and $\mu$ is the linear mass density.Since $T$ and $\mu$ are constant,we have $f \propto \frac{1}{L}$,which implies $fL = 	ext{constant} = k$.Therefore,$L = \frac{k}{f}$.When the wire of length $L$ is divided into three segments of lengths $L_1, L_2, L_3$,we have $L = L_1 + L_2 + L_3$.Substituting $L = \frac{k}{f}$,$L_1 = \frac{k}{f_1}$,$L_2 = \frac{k}{f_2}$,and $L_3 = \frac{k}{f_3}$ into the equation,we get:$\frac{k}{f} = \frac{k}{f_1} + \frac{k}{f_2} + \frac{k}{f_3}$.Dividing both sides by $k$,we obtain the relation: $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3}$.

When a stretched wire of fundamental frequency $f$ is divided into three segments,the fundamental frequencies of these three segments are $f_1, f_2$ and $f_3$ respectively. Then the relation among $f_1, f_2, f_3$ and $f$ is (Assume tension is constant).

Similar Questions

Two wires of the same material with radii $r$ and $2r$ respectively are welded together end to end. The combination is then used as a sonometer wire under tension $T$. The joint is kept midway between the two bridges. The ratio of the number of loops in the wires,given that the joint is a node,is:

$A$ string is under tension of $180 \ N$ and mass per unit length $2 \times 10^{-3} \ kg/m$. It produces two consecutive resonant frequencies with a tuning fork,which are $375 \ Hz$ and $450 \ Hz$. The mass of the string is: (in $g$)

Two identical strings of length $\ell$ and $2\ell$ vibrate with fundamental frequencies $N$ Hz and $1.5N$ Hz,respectively. The ratio of tensions for the smaller length to the larger length is

$A$ second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The points where the string has to be plucked and touched are

Obtain the equation of frequency of oscillations in a string tied at both ends.

Vedclass Test Series

Exam Paper Generator

Online Exam Module