In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to (3/4) th of the original length and the tension is changed. The factor by which the tension is to be changed is

Question

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to (3/4) th of the original length and the tension is changed. The factor by which the tension is to be changed is (A) (3/8) (B) (2/3) (C) (8/9) (D) (9/4)

Tardigrade Admin · Accepted Answer

n=(1/2 l) √(T/m) ⇒ n propto (√T/l) ⇒ (T2/T1)=((n2/n1))2((l2/l1))2 =(2)2((3/4))2=(9/4)

Q. In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4}$ th of the original length and the tension is changed. The factor by which the tension is to be changed is

$\frac{3}{8}$

$\frac{2}{3}$

$\frac{8}{9}$

$\frac{9}{4}$

$n = \frac{1}{2 l} \frac{T}{m}$
$\Rightarrow n \propto \frac{T}{l}$
$\Rightarrow \frac{T _{2}}{T _{1}} = (\frac{n _{2}}{n _{1}})^{2} (\frac{l _{2}}{l _{1}})^{2}$
$= (2)^{2} (\frac{3}{4})^{2} = \frac{9}{4}$

Q. In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to 43​ th of the original length and the tension is changed. The factor by which the tension is to be changed is

83​

32​

98​

49​