A tuning fork gives 5 beats per second with a 33 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 the frequency of the tuning fork be n . The frequency of a sonometer wire is inversely proportional to its length, f 1 L . Let f₁ and f₂ be the frequencies of the wire for lengths L₁ = 33 cm and L₂ = 32 cm respectively. Since L₂ f₁ . The tuning fork gives 5 beats per second with both lengths. Thus, f₁ must be less than n and f₂ must be greater than n . n - f₁ = 5 f₁ = n - 5 f₂ - n = 5 f₂ = n + 5 Using the relation f₁ L₁ = f₂ L₂ : (n - 5) 33 = (n + 5) 32 33n - 165 = 32n + 160 n = 325 Hz Answer: 325 Hz