Physics-
General
Easy
Question
An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
The correct answer is: ![200 s to the power of negative 1 end exponent](data:image/png;base64,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)
Frequency of second overtone (fifth harmonic) of close pipe
![equals fraction numerator 5 v over denominator f l end fraction](data:image/png;base64,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)
Frequency of first overtone (second harmonic) of open pipe
![equals fraction numerator 2 v over denominator 2 l end fraction](data:image/png;base64,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)
Accordingly,
![fraction numerator 5 v over denominator 4 l end fraction minus fraction numerator 2 v over denominator 2 l end fraction equals 100](data:image/png;base64,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)
Or
![fraction numerator v over denominator 4 l end fraction equals 100](data:image/png;base64,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)
Or
![v equals 400 blank l](data:image/png;base64,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)
Fundamental frequency of open pipe
![equals fraction numerator v over denominator 2 l end fraction equals fraction numerator 400 l over denominator 2 l end fraction equals 200 s to the power of negative 1 end exponent](data:image/png;base64,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)
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