Two vibrating strings of the same material bu | vedclass

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

Question

(D) The fundamental frequency $n$ of a vibrating string is given by the formula: $n = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$,where $\mu$ is the mass per u

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) The fundamental frequency $n$ of a vibrating string is given by the formula: $n = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$,where $\mu$ is the mass per unit length.Since $\mu = \pi r^2 ho$ (where $ho$ is the density of the material),the frequency is $n = \frac{1}{2lr} \sqrt{\frac{T}{\pi ho}}$.Given that the material is the same,$ho$ is constant. Since the tension $T$ is also the same,we have $n \propto \frac{1}{lr}$.Therefore,the ratio of the frequencies is $\frac{n_1}{n_2} = \frac{l_2 r_2}{l_1 r_1}$.Substituting the given values: $l_1 = L$,$l_2 = 2L$,$r_1 = 2r$,and $r_2 = r$.$\frac{n_1}{n_2} = \frac{2L 	imes r}{L 	imes 2r} = \frac{2Lr}{2Lr} = 1$.

Similar Questions

If we add $3 \ kg$ load to the hanger of a sonometer,the fundamental frequency becomes two times its initial value. The initial load must be (in $kg$)

$A$ stretched string resonates with a tuning fork of frequency $512 \; Hz$ when the length of the string is $0.5 \; m$. The length of the string required to vibrate resonantly with a tuning fork of frequency $256 \; Hz$ would be .......... $m$.

The frequency of a sonometer wire is $f$. When the weights producing the tension are completely immersed in water,the frequency becomes $f/2$. When the weights are immersed in a certain liquid,the frequency becomes $f/3$. The specific gravity of the liquid is:

The fundamental frequency of a sonometer wire increases by $6\, Hz$ if its tension is increased by $44\%$,keeping the length constant. The frequency of the wire is ...... $Hz$.

$A$ tuning fork is sounded with a sonometer wire of length $95 \, cm$ or $100 \, cm$,producing $4$ beats per second in both cases. What is the frequency of the tuning fork in $Hz$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module