The fundamental frequency of sonometer wire is ' n '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be

Step-by-step solution

The fundamental frequency of a sonometer wire is given by n = 1 2L T , where L is the length, T is the tension, and is the linear mass density. Expressing in terms of material density and diameter d , we have = ( d^2 4 ) . Substituting yields n = 1 2L 4T d^2 = 1 Ld T , establishing the proportionality n 1 Ld T . With the new parameters L' = 3L , T' = 3T , and d' = 2d , the frequency ratio becomes: n' n = Ld L'd' T' T = Ld (3L)(2d) 3T T = 1 6 3 Thus n' = 3 6 n = 1 2 3 n , which corresponds to option C .