First overtone frequency of a closed pipe of length ' ( l₁ ^ ) is equal to ( 2^ nd ) hormonic frequency of an open pipe of length ' ( l₂ ) '. The ratio ( l₁ l₂ ) is

Step-by-step solution

Given, first overtone frequency of closed pipe of length ( l₁=2^ nd ) harmonic frequency of on open pipe of length ( l₂ ) Now, first overtone frequency of close pipe ( 3 u 4 l₁ ) ( 2^ nd ) harmonic frequency of open pipe ( = 2 u 2 l₂ ) ( 3 u 4 l₁ = 2 u 2 l₁ ) On rearranging, we get ( l₁ l₂ = 3 u 4 1 u = 3 4 ) Therefore, ratio is ( l₁ l₂ = 3 4 ).