A sonometer wire has a length of 115 cm between its two fixed ends. Determine the positions where the two bridges can be placed so that the fundamental frequencies of the three segments so formed are in the ratio of 1 : 4 : 20.

A sonometer wire has a length of 115 cm between its two fixed ends. De

1.	A sonometer wire has a length of 115 cm between its two fixed ends. Determine the positions where the two bridges can be placed so that the fundamental frequencies of the three segments so formed are in the ratio of 1 : 4 : 20.
Answer» Solution :Given, total length of the SONOMETER wire, L = 115 cm `v_(1) : v_(2) : v_(3) = 1 : 4 : 20` If `L_(1), L_(2) and L_(3)` are the lengths of three parts and `v prop (1)/(L)` Then, `L_(1) : L_(2) : L_(3) = (1)/(1) : (1)/(4) : (1)/(20) = 20 : 5 : 1` Sum of ratios = 20 + 5 + 1 = 26 `therefore""L_(1) = (20)/(26) xx 115 = 88.46` cm `L_(2) = (5)/(26) xx 115 = 22.12` cm `L_(3) = (1)/(26) xx 115 = 4.42` cm So, the bridges should be placed at 88.46 cm and 110.58 cm from ONE end.