In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to 3 4 th of the original length and the tension is changed. The factor by which the tension is to be changed is

Step-by-step solution

Frequency of stretched string. n = 1 2 l T m aligned & n T l & n₁ n₂ = l₂ I₁ T₁ T₂ n 2 n = 3 4 l T₁ T₂ & 1 2 = 3 4 T₁ T₂ T₁ T₂ = 2 3 & T₁ T₂ = 4 9 T₂= 9 4 T₁ aligned Tension should be changed by the factor 9 4 .