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String Fixed at Both Ends

If f1, f2, ...

Question

If $f_{1}, f_{2}, a n d f_{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $f_{0}$ of the whole string is

f_{0} = f_{1} + f_{2} + f_{3}

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\frac{1}{f_{0}} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}

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\frac{1}{\sqrt{f_{0}}} = \frac{1}{\sqrt{f_{1}}} + \frac{1}{\sqrt{f_{2}}} + \frac{1}{\sqrt{f_{3}}}

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None of these

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Solution

The correct option is B $\frac{1}{f_{0}} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}$
The original fundamental frequency is the harmonic mean.
$\frac{1}{f_{0}} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}$
This happens because we sum up the individual wavelengths and equate it to the final wavelength.
$λ = \frac{v}{f}$

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