Two pipes of lengths L ₁ and L ₂ , open at both ends are joined in series. If ' f₁ ' and ' f₂ ' are the fundamental frequencies of two pipes, then the fundamental frequency of series combination will be (neglect end correction)

Step-by-step solution

Fundamental frequency for an open pipe is given by f = v 2L , where v is the speed of sound and L is the pipe length. The individual pipe lengths are L₁ = v 2f₁ and L₂ = v 2f₂ . When joined in series, the total length becomes L_ total = L₁ + L₂ = v 2 ( 1 f₁ + 1 f₂ ) = v 2 f₁ + f₂ f₁ f₂ . The fundamental frequency of the combined pipe is then: f_ total = v 2L_ total = v 2 v 2 f₁ + f₂ f₁ f₂ = 1 f₁ + f₂ f₁ f₂ = f₁ f₂ f₁ + f₂ . The result corresponds to option C .