An organ pipe P ₁ closed at one end has vibrating air column in its first overtone and another pipe P ₂ open at both ends has vibrating air column in the third overtone, which are in resonance with a given tuning fork. The ratio of the length of pipe P₁ to that of P₂ is

Step-by-step solution

Since, both pipes are in resonance with a given tuning fork, therefore, they will have the same frequency of vibration. For the organ pipe closed at one end. First overtone (n=3) , . For organ pipe open at both ends, Third overtone (n=4) , From (1) and (2) aligned & 3 v 4 l₁ = 4 v 2 l₂ & l₁ l₂ = 3 8 aligned