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String Fixed at Both Ends

If n 1,n2,n3...

Question

If n $_{1}, n_{2}, n_{3}$ are the three fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency ' $n$ ' of the string is given by

\sqrt{n} = \sqrt{n_{1}} + \sqrt{n_{2}} + \sqrt{n_{3}}

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\frac{1}{\sqrt{n}} = \frac{1}{\sqrt{n_{1}}} + \frac{1}{\sqrt{n_{2}}} + \frac{1}{\sqrt{n_{3}}}

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n = n_{1} + n_{2} + n_{3}

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\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}

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Solution

The correct option is C $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$
Total length of string is $l = l_{1} + l_{2} + l_{3}$
but $f \propto \frac{1}{l}$
$\Rightarrow \frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}$

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If n1,n2,n3 are the three fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency 'n' of the string is given by

The correct option is C 1n=1n1+1n2+1n3Total length of string is l=l1+l2+l3but f∝1l⇒1f=1f1+1f2+1f3

If n $_{1}, n_{2}, n_{3}$ are the three fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency ' $n$ ' of the string is given by

The correct option is C $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$
Total length of string is $l = l_{1} + l_{2} + l_{3}$
but $f \propto \frac{1}{l}$
$\Rightarrow \frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}$