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

Step-by-step solution

Recall the formula of fundamental frequency in terms of tension and mass per unit length, f = 1 2 l T μ it means, f 1 f 2 = 1 2 l 1 T 1 μ f = 1 2 l 2 T 2 μ = l 2 l 1 × T 1 T 2 Put given data, 1 2 = l 1 - x 100 l × T T 1 + 44 100 ⇒ 1 2 = 100 - x 10 × 1 12 ⇒ 60 = 100 - x ⇒ x = 40