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  • How to solve this problem- If n1, n2and n3 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:

If n1, n2 and n3 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:

  • Option 1)

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

  • Option 2)

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

  • Option 3)

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

  • Option 4)

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

 

Answers (1)

best_answer

As we learnt in 

Fundamental frequency with end correction -

u _{0}= frac{V}{4left ( l+e ight )}     (one end open)

u _{0}= frac{V}{2left ( l+2e ight )}    (Both end open)

e = end correction

-

 n= \frac{1}{2l}\sqrt{\frac{T}{m}}

n\propto \frac{1}{l} \ or \ nl=K

n_1l_1 = k

n_2l_2 = k

n_3l_3 = k

l = l_1+l_2+l_2

\frac{k}{n}=\frac{k}{n_1}+\frac{n}{n_2}+\frac{k}{n_3}

\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}


Option 1)

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

Correct

Option 2)

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

Incorrect

Option 3)

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

Incorrect

Option 4)

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

Incorrect

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perimeter

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