Question

The second overtone of an open organ pipe has the same frequency as the 1st overtone  of a closed pipe L metre long. Then what will be the length of the open pipe.

Answer 1

2^nd  overtone of an open organ pipe = \(\frac{3v}{2L_0}\)

1^st overtone of an closed organ pipe = \(\frac{3v}{4L_C}\)

\(\frac{3v}{3L_0} = \frac{3v}{4L_C}\)

\(\frac{1}{L_0}\) = \(\frac{1}{2L_C}\)

L₀ = 2L_C

The length of the open pipe is two times of the length of the closed pipe