A string is stretched so that its length is i | vedclass

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

Question

(D) The fundamental frequency of transverse vibration is given by $f_T = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $T$ is tension,$L$ is length,and $\m

Vedclass · Accepted Answer

$1:\sqrt{\eta }$

Vedclass · Answer

(D) The fundamental frequency of transverse vibration is given by $f_T = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $T$ is tension,$L$ is length,and $\mu$ is mass per unit length.The fundamental frequency of longitudinal vibration is given by $f_L = \frac{1}{2L} \sqrt{\frac{Y}{\rho}}$,where $Y$ is Young's modulus and $\rho$ is density.Using $Y = \frac{T/A}{\Delta L/L}$,we have $\frac{Y}{\rho} = \frac{T}{\rho A} \cdot \frac{L}{\Delta L} = \frac{T}{\mu} \cdot \frac{L}{\Delta L}$.Thus,$\frac{f_T}{f_L} = \sqrt{\frac{T/\mu}{Y/\rho}} = \sqrt{\frac{T/\mu}{(T/\mu) \cdot (L/\Delta L)}} = \sqrt{\frac{\Delta L}{L}}$.Given $\frac{\Delta L}{L} = \frac{1}{\eta}$,the ratio is $\sqrt{\frac{1}{\eta}} = \frac{1}{\sqrt{\eta}}$.

$A$ string is stretched so that its length is increased by $\frac{1}{\eta }$ of its original length. The ratio of the fundamental frequency of transverse vibration to that of the fundamental frequency of longitudinal vibration will be

Similar Questions

The ratio of the speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is

The speed of sound in oxygen $(O_2)$ at a certain temperature is $460 \,ms^{-1}$. The speed of sound in helium $(He)$ at the same temperature will be (assume both gases to be ideal): (in $\,ms^{-1}$)

The figure below shows pressure variation in two different sound waves in air with time at a given position. Both the figures are drawn to the same scale. Which of the following statements is true?

What is called compression or condensation? Which type of changes in density and pressure take place in it?

Vedclass Test Series

Exam Paper Generator

Online Exam Module