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

Total length of string l = l1+l2+l3(As string is divided into three segments)n1  = 12l1Tμ; n2 = 12l2Tμ; n3 = 12l3TμHence frequency ∝ 1length(∵ n = 12lTm)∴  1n= 2lTμ = 2l1Tμ+2l2Tμ+2l3Tμ = 1n1+1n2+1n3