The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by 25 % by keeping tension same then frequency change of second harmonic is

Step-by-step solution

The fundamental frequency of a sonometer wire is given by f = 1 2L T , where L is the length, T is the tension, and is the linear mass density. With an initial fundamental frequency of 50 Hz, increasing the length by 25% gives L₂ = 5 4 L₁ . Since tension and linear mass density remain constant, the new fundamental frequency becomes f₁' = 1 2L₂ T = 1 2(5L₁/4) T = 4 5 50 = 40 Hz. The second harmonic frequency is always twice the fundamental frequency. Initially f_ 2, initial = 2 50 = 100 Hz, and after the change f_ 2