The fundamental frequency of an open organ pipe P₂ is identical to the first overtone frequency of a closed organ pipe P₁ . If pipe P₁ has a length of 30 cm , what is the length of P₂ ?

Step-by-step solution

For a closed organ pipe P₁ of length L₁ , the first overtone frequency is given by f₁ = 3v 4L₁ For an open organ pipe P₂ of length L₂ , the fundamental frequency is given by f₂ = v 2L₂ Given that f₁ = f₂ 3v 4L₁ = v 2L₂ L₂ = 2L₁ 3 Substituting L₁ = 30 cm L₂ = 2 30 3 = 20 cm