If n1, n2 and n3 are the fundamental frequencies of three

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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 :

n =	1	√	T
	2l		m

or, n ∝	1	or nl = constant, K
	l

∴ n₁l₁ = K,
n₂l₂ = K, n₃l₃ = K
Also, l = l₁ + l₂ +l₃

or,	K	=	K	+	K	+	K
	n		n₁		n₂		n₃

or,	1	=	1	+	1	+	1
	n		n₁		n₂		n₃

1	=	1	+	1	+	1
√n	=	√n₁	+	√n₂	+	√n₃