The fundamental frequency of sound produced in an open pipe of length L ₁ is same as the frequency of the 3^ rd harmonic of the sound produced in the closed pipe of length L _ 2 Then the ratio of L _ 1 L _ 2 is :

Step-by-step solution

The fundamental frequency of an open pipe of length L₁ is given by f₁ = v 2L₁ , where v is the speed of sound. The frequencies of a closed pipe of length L₂ are given by f_n = nv 4L₂ , where n is an odd integer ( n = 1, 3, 5, ). The 3^ rd harmonic of a closed pipe corresponds to the 3^ rd overtone frequency, which is the 5^ th harmonic ( n=5 ). However, in many contexts, the 3^ rd harmonic of a closed pipe is simply the 3^ rd allowed frequency, which corresponds to n=5 . Let us verify the standard terminology: the