Question

Let $n_1,n_2,n_3....$are the frequencies of segments of a stretched string, then the frequency $n$ of the string can be given by

• A. $n=n_1+n_2+n_3+.....$
• B. $n=\sqrt{n_1\times n_2\times n_3\times ....}$
• C. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}+....$
• D. None of the above

Answer 1

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

We know that for a vibrating string
$n_1{l}_1=n_2{l}_1=n_3{l}_3....=k\left(constant\right)=nl$
Also, $l_1+l_2+l_3+....=1$
$\therefore \frac{k}{n_1}+\frac{k}{n_2}+\frac{k}{n_3}....=\frac{k}{n}$
$=\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}+......$