The fundamental frequency of a transverse wav | vedclass

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

Question

(D) The fundamental frequency $f$ of a stretched string is given by the formula: $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $L$ is the length,$T$ i

Vedclass · Accepted Answer

$4: 9$

Vedclass · Answer

(D) The fundamental frequency $f$ of a stretched string is given by the formula: $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $L$ is the length,$T$ is the tension,and $\mu$ is the linear mass density.Given $f_1 = 300 \ Hz$,$L_1 = L$,and $T_1 = T_1$. Thus,$300 = \frac{1}{2L} \sqrt{\frac{T_1}{\mu}}$.Given $f_2 = 100 \ Hz$,$L_2 = 2L$,and $T_2 = T_2$. Thus,$100 = \frac{1}{2(2L)} \sqrt{\frac{T_2}{\mu}} = \frac{1}{4L} \sqrt{\frac{T_2}{\mu}}$.Dividing the two equations: $\frac{300}{100} = \frac{\frac{1}{2L} \sqrt{\frac{T_1}{\mu}}}{\frac{1}{4L} \sqrt{\frac{T_2}{\mu}}}$.$3 = \frac{4L}{2L} \sqrt{\frac{T_1}{T_2}} = 2 \sqrt{\frac{T_1}{T_2}}$.$1.5 = \sqrt{\frac{T_1}{T_2}}$.Squaring both sides: $2.25 = \frac{T_1}{T_2}$,which is $\frac{9}{4} = \frac{T_1}{T_2}$.Therefore,$\frac{T_2}{T_1} = \frac{4}{9}$.

Similar Questions

$A$ tuning fork produces $4$ beats per second when sounded with a sonometer wire of vibrating length $48 \ cm$. It also produces $4$ beats per second when the vibrating length is $50 \ cm$,keeping the tension in the wire the same. What is the frequency of the tuning fork in $Hz$?

$A$ tuning fork gives $4$ beats with $50 \, cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \, cm$,the number of beats remains the same. The frequency of the fork is ............. $Hz$.

$A$ string is stretched between fixed points separated by $75.0\, cm$. It is observed to have resonant frequencies of $420\, Hz$ and $315\, Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is .... $Hz$

The frequency of a sonometer wire is $100 \ Hz$. When the weights producing the tension are completely immersed in water,the frequency becomes $80 \ Hz$,and on immersing the weights in a certain liquid,the frequency becomes $60 \ Hz$. The specific gravity of the liquid is:

$A$ wire of length $1 \,m$ under a certain initial tension emits a sound of fundamental frequency $256 \,Hz$. When the tension is increased by $1 \,kg \,wt$,the frequency of the fundamental note increases to $320 \,Hz$. The initial tension is ........... $kg \,wt$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module