A tuning fork gives 5 beats per second with 40 cm length of sonometer wire. If the length of the wire is shortened by 1 cm , the number of beats is still the same. The frequency of the fork is

Step-by-step solution

Let f_t be the tuning fork frequency. For a sonometer wire, frequency is inversely proportional to length ( f 1/L ), yielding fL = constant . With L₁ = 40 cm and L₂ = 39 cm , we have f₁ 40 = f₂ 39 , so f₂ = 40 39 f₁ . Beat frequencies are |f_t - f₁| = 5 and |f_t - f₂| = 5 . Since f₂ > f₁ , the tuning fork frequency must lie between them to maintain equal beat differences, giving f_t = f₁ + 5 and f_t = f₂ - 5 . Equating these expressions: f₁ + 5 = f₂ - 5 , so f₂ = f₁ + 10 . Substituting 40 39 f₁ = f₁ + 10 gives 1 39