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Question:

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe 2m long. The length of the open pipe is: 4 m, 1 m, 2 m, 8 m

8 m

1 m

4 m

2 m

Solution:

Given : Length of the closed pipe L'=2m
First overtone frequency of closed pipe ν'=3v/4L'
Let the length of the open organ pipe be L
Second overtone of an open pipe i.e m=3 ν3=3v/2L
But ν3=ν'
∴3v/2L=3v/4L'
⇒L=2L'=2×2=4m