Question

stretched string is taken and stretched such that elongated by 1% then the fundamental frequency

Answer 1

A string is stretched so that its length is increased by η1 of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be. A .

Answer 2

Given that,

Elongation = 1%

Suppose the length of the string is l m and fundamental frequency is 2 Hz then the string stretched such that elongated by 1% .

We need to calculate the length after stretched

Using formula of length

$l'=l+0.001l$

$l'= 1.001l$

We know that,

Fundamental frequency  :

Fundamental frequency  is inversely proportional of length of string.

$n\propto\dfrac{1}{l}$

We need to calculate the fundamental frequency

Using formula of fundamental frequency

$\dfrac{n_{1}}{n_{2}}=\dfrac{l'}{l}$

Put the value into the formula

$\dfrac{2}{n_{2}}=\dfrac{1.001l}{l}$

$n_{2}=\dfrac{2}{1.001}$

$n_{2}=1.9\ Hz$

Hence, The fundamental frequency  is 1.9 Hz