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:
If $n_1$ origin

• 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 $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

$n_1=\frac{1}{2l_1}\sqrt{\frac{T}{\mu }}{n}_2=\frac{1}{2l_2}\sqrt{\frac{T}{\mu }}{n}_3=\frac{1}{2l_3}\sqrt{\frac{T}{\mu }}n=\frac{1}{2l}\sqrt{\frac{T}{\mu }}l=l_1+l_2+l_3\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$