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Vibrations of a stretched string
Appears in
Concepts tested here
- Law of length 2
All Questions
2014 AIPMT 1 question
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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:Total length of string $l = l_1 + l_2 + l_3$
Frequency $\propto \frac{1}{\text{length}}$
So $\frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3}$
2012 AIPMT-PRE 1 question
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When a string is divided into three segments of length $l_1$, $l_2$ and $l_3$, the fundamental frequencies of these three segments are $\nu_1$, $\nu_2$ and $\nu_3$ respectively. The original fundamental frequency ($\nu$) of the string isFundamental frequency of a string: $\nu = \frac{v}{2l} \Rightarrow l = \frac{v}{2\nu}$
Similarly $l_1 = \frac{v}{2\nu_1}$, $l_2 = \frac{v}{2\nu_2}$, $l_3 = \frac{v}{2\nu_3}$
$l = l_1 + l_2 + l_3 \Rightarrow \frac{v}{2\nu} = \frac{v}{2\nu_1} + \frac{v}{2\nu_2} + \frac{v}{2\nu_3}$
$\frac{1}{\nu} = \frac{1}{\nu_1} + \frac{1}{\nu_2} + \frac{1}{\nu_3}$