If the length of a stretched string is shortened by 40 % and the tension is increased by 44 % , then the ratio of the final and initial fundamental frequencies is :

Step-by-step solution

Fundamental frequency, n= 1 2 l T m Initial frequency, n₁= 1 2 l T m New length, l^ =l- l 40 100 =0.6 l New tension, T^ =T+ T 44 100 =1.44 ~T New frequency n₂= 1 2 l^ T^ m n₂ n₁ = 1 2 l^ T^ m 1 2 l T m n₂ n₁ = l l^ ( T^ T ) = l 0.6 l 1.44 T T = 1 0.6 1.2=2 n₂: n₁=2: 1