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

Question

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

Infinity Learn · Accepted Answer

$$n1=12l1T$$μ                       . . . .  (i)n2=12l2T$$μ                               . . . . .$$(ii)n3=12l3T$$μ                          . . . . . $$(iii) $$andn=12lT$$μ                        . . . . . (iv) From eqn. (iv), we get $$1n=2lT$$μ As $$l=l1+l2+l3$$∴  $$1n=2l1+l2+l3T$$μ$$=2l1T$$μ$$+2l2T$$μ$$+2l3T$$μ$$=1n1+1n2+1n3$$ (using$$ $$(i), (ii) and (iii))

If $n_{1}, n_{2} a n d n_{3}$ 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

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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

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If $n_{1}, n_{2} a n d n_{3}$ 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