A string is divided into three segments, so that the segment possesses fundamental frequencies in the ratio 1: 2: 3 . Then, the length of the segments are in the ratio

Step-by-step solution

Given, ratio of fundamental frequencies be f₁: f₂: f₃=1: 2: 3 Let ratio of length be l₁: l₂: l₃ . Since, f= 1 2 l T where, f is frequency, l is length of string, T is tension and is mass per unit length. l 1 f So, l₁: l₂: l₃= 1 f₁ : 1 f₂ : 1 f₃ = 1 1 : 1 2 : 1 3 = 6 6 : 3 6 : 2 6 =6: 3: 2