If the length of stretched string is reduced by 40 % and tension is increased by 44 % then the ratio of final to initial frequencies of stretched string is

Step-by-step solution

Let the initial length and tension be l and T respectively. After shortening, The new length l_ new =l- 40 100 l= 3 5 l After increase in tension, the new tension T _ new = T + 44 100 ~T = 144 ~T 100 Fundamental frequency of a vibrating string is given by aligned n & = 1 2 l T m n ₁ & = 1 2 l T m n ₂ & = 1 2 l T _ new m n ₁ n ₂ & = l aew l T T _ new & = 3 5 l l 100 ~T 144 ~T & = 3 5 10 12 = 1 2 n ₂ n ₁ & = 2 1 aligned