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 follows n = 1 2L T , where = d^2 4 for a wire of diameter d and material density . Substituting gives n = 1 Ld T , so n T Ld . With L tripled, T tripled, and d doubled, the new frequency n₂ satisfies n₂ n = L d (3L)(2d) 3T T = 1 6 3 . n₂ = 3 6 n = n 2 3 , matching option C.