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

n1=12l1Tμ                       . . . .  (i)n2=12l2Tμ                               . . . . .(ii)n3=12l3Tμ                          . . . . . (iii) andn=12lTμ                        . . . . . (iv) From eqn. (iv), we get 1n=2lTμ As l=l1+l2+l3∴  1n=2l1+l2+l3Tμ=2l1Tμ+2l2Tμ+2l3Tμ=1n1+1n2+1n3 (using (i), (ii) and (iii))