If the frequency of vibrations of a string is | vedclass

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

Question

(C) The frequency of vibration of a stretched string is given by the formula $n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $n$ is the frequency,$L$ is

Vedclass · Accepted Answer

Four times

Vedclass · Answer

(C) The frequency of vibration of a stretched string is given by the formula $n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $n$ is the frequency,$L$ is the length,$T$ is the tension,and $\mu$ is the linear mass density.From this relation,we can see that $n \propto \sqrt{T}$.If the frequency is increased by a factor of two,the new frequency $n' = 2n$.Therefore,$\frac{n'}{n} = \frac{\sqrt{T'}}{\sqrt{T}} = 2$.Squaring both sides,we get $\frac{T'}{T} = 4$,which implies $T' = 4T$.Thus,the tension must be made four times the original tension.

If the frequency of vibrations of a string is to be increased by a factor of two,then the tension in the string must be made:

Similar Questions

$A$ tuning fork produces $5 \, Hz$ beats per second when the length of a sonometer wire is either $1 \, m$ or $1.05 \, m$. Calculate the frequency of the tuning fork in $Hz$.

The frequency of transverse vibrations in a stretched string is $200 \ Hz$. If the tension is increased four times and the length is reduced to one-fourth the original value,the frequency of vibration will be .... $Hz$.

To increase the frequency of a stretched string from $100 \ Hz$ to $400 \ Hz$,the tension in the string has to be changed by how many times?

$A$ sonometer wire under suitable tension having specific gravity $\varrho$,vibrates with frequency $n$ in air. If the load is completely immersed in water,the frequency of vibration of the wire will become:

Vedclass Test Series

Exam Paper Generator

Online Exam Module