The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1: 3: 5.

Let L(=100 cm) be the length of the wire and L1,L2 and L3 are the lengths of the segments as shown in the figure.  Fundamental frequency, v∝1L  As the fundamental frequencies are in the ratio of 1:3 : 5, ∴  L1:L2:L3=11:13:15=15:5:3  Let x be the common factor. Then 15 x+5 x+3 x=L=100 23x=100   or   x=10023 ∴  L1=15×10023=150023 cm         L2=5×10023=50023 cm         L3=3×10023=30023 cm ∴ The bridges should be placed from A at 150023 cm and 200023 cm respectively.