If the length of a stretched string is shortened by x % and the tension is increased by 44 % . Then the ratio of the final and initial fundamental frequencies is 1: 2 , then the value of x is

Step-by-step solution

Fundamental frequency for string, n= 1 2 l T m So, n T / l Now, T^ =T+0.44 T= 144 T 100 and l^ =l- x 100 l= ( 100-x 100 ) l Also, n^ n = 2 1 2 1 = 144 T 100 T l ( 100-x 100 ) l = 12 10 100 100-x or (100-x)=60 or x=40