Waves - Result Question 44
46. 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 :
[2014, 2012, 2000]
(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) $n=n_1+n_2+n_3$
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Answer:
Correct Answer: 46. (a)
Solution:
- (a)
$n=\frac{1}{2 l} \sqrt{\frac{T}{m}}$ or, $n \propto \frac{1}{l}$ or $n l=$ constant, $K$
$\therefore n_1 l_1=K$
$n_2 l_2=K, n_3 l_3=K$
Also, $l=l_1+l_2+l_3$
or, $\frac{K}{n}=\frac{K}{n_1}+\frac{K}{n_2}+\frac{K}{n_3}$
or, $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
