A sonometer wire has a length of 114 ~cm , between two fixed ends. Where should two bridges be placed so as to divide the wire into three segments (in cm ) whose fundamental frequencies are in the ratio 1: 3: 4 ?

Step-by-step solution

If length of the wire between the two bridges is l , the frequency of vibration n= 1 2 l T m n 1 l Therefore, n₁: n₂: n₃= 1 l₁ : 1 l₂ : 1 l₃ n₁: n₂: n₃= 1 114 1 8 : 1 114 3 8 : 1 114 4 8 or n₁: n₂: n₃=8: 8 3 : 2 or n₁: n₂: n₃=72: 24: 18