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Byju's Answer

Standard XII

Mathematics

nth Term of A.P

If n1, n2, n3...

Question

If $n_{1}, n_{2}, n_{3}$ are the fundamental frequencies of three segments of a stretched string, find the fundamental frequency of the string.

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Solution

Here, $n_{1} = \frac{v}{2 l_{1}} n_{2} = \frac{v}{2 l_{2}} n_{3} = \frac{v}{2 l_{3}}$

Total length of the string, $l = l_{1} + l_{2} + l_{3} = \frac{v}{2 n_{1}} + \frac{v}{2 n_{2}} + \frac{v}{2 n_{3}}$

So, fundamental frequency of the string, $n = \frac{v}{2 l} = \frac{1}{\frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}}$

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If n1, n2, n3 are the fundamental frequencies of three segments of a stretched string, find the fundamental frequency of the string.

Here, n1=v2l1n2=v2l2n3=v2l3 Total length of the string, l=l1+l2+l3=v2n1+v2n2+v2n3 So, fundamental frequency of the string, n=v2l=11n1+1n2+1n3

If $n_{1}, n_{2}, n_{3}$ are the fundamental frequencies of three segments of a stretched string, find the fundamental frequency of the string.