The first over tone of an open organ pipe has the same frequency as the first overtone of a closed pipe 3.6 m in length. What is the length of the open organ pipe?
Solution
Given Length of the closed pipe = L = 3.6 m
Assume Frequency of the first overtone of the open pipe = f
Frequency of the first overtone of the closed pipe = f’
This question is solved wrong. The first overtone of a closed organ pipe is the second harmonic, whose frequency is
f’ = 3v / 4L’
While the first overtone of an open organ pipe is also its second harmonic, and its frequency is given by
f” = v / L”
According to given conditions, the first overtones of both the pipes are equal, so
f’ = f”
3v / 4L’ = v / L”
Which, upon simplification, leads to
L” = 4L’ / 3
And by putting values, the length of the open organ pipe is 4.8 m.
(Kindly make corrections so as others won’t be confused.)
This question is solved wrong. The first overtone of a closed organ pipe is the second harmonic, whose frequency is
f’ = 3v / 4L’
While the first overtone of an open organ pipe is also its second harmonic, and its frequency is given by
f” = v / L”
According to given conditions, the first overtones of both the pipes are equal, so
f’ = f”
3v / 4L’ = v / L”
Which, upon simplification, leads to
L” = 4L’ / 3
And by putting values, the length of the open organ pipe is 4.8 m.
(Kindly make corrections so as others won’t be confused.)
The question on the book is wrong we know that first overtone is 2nd harmonic frequency but written of book take it as 1st harmonic frequency
Yes the question on the book is wrong
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