An organ pipe of length L open at both ends i | vedclass

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(B) For an open organ pipe,the frequency of the first harmonic (fundamental frequency) is given by:$f = \frac{v}{2L} = 480 \, Hz$For a pipe closed at

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$\frac{L}{2}$

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(B) For an open organ pipe,the frequency of the first harmonic (fundamental frequency) is given by:$f = \frac{v}{2L} = 480 \, Hz$For a pipe closed at one end,the frequency of the first harmonic (fundamental frequency) is given by:$f' = \frac{v}{4L'} = 480 \, Hz$Since the tuning fork is the same,$f = f'$,therefore:$\frac{v}{2L} = \frac{v}{4L'}$By simplifying the equation:$4L' = 2L$$L' = \frac{2L}{4} = \frac{L}{2}$Thus,the length of the pipe closed at one end should be $\frac{L}{2}$.

An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480 \, Hz$. What should be the length of a pipe closed at one end,so that it also vibrates in its first harmonic with the same tuning fork?

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