Question

If $n_1,n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

• A. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
• B. $\frac{1}{\sqrt{n}}=\frac{1}{{\sqrt{n}}_1}+\frac{1}{{\sqrt{n}}_2}+\frac{1}{{\sqrt{n}}_3}$
• C. $\sqrt{n}={\sqrt{n}}_1+{\sqrt{n}}_2+{\sqrt{n}}_3$
• D. $n=n_1+n_2+n_3$

Answer 1

The correct option is A $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

$n_1=\frac{1}{2l_1}\sqrt{\frac{T}{\mu }}$
$n_2=\frac{1}{2l_2}\sqrt{\frac{T}{\mu }}$
$n_3=\frac{1}{2l_3}\sqrt{\frac{T}{\mu }}$
$n=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
$l=l_1+l_2+l_3$
$\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$