A tuning fork produces 6 beats per second with both, 60 cm and 40 cm of the stretched wire of sonometer. The frequency of fork is

Step-by-step solution

Let the frequency of the tuning fork be n . The frequency of a stretched sonometer wire is given by f = v 2L , which implies f 1 L . Let f₁ and f₂ be the frequencies of the wire of lengths L₁ = 60 cm and L₂ = 40 cm respectively. Since L₁ > L₂ , we have f₁ The tuning fork produces 6 beats per second with both lengths. Thus, n must lie between f₁ and f₂ . n - f₁ = 6 f₁ = n - 6 f₂ - n = 6 f₂ = n + 6 Since f 1 L , we have f₁ L₁ = f₂ L₂ . Substituting the values: (n - 6) 60 = (n + 6) 40 3(n - 6) = 2(n + 6) 3n - 18 = 2n