How to solve the following question?

An open organ pipe has two adjacent natural frequencies of 500 and 600 Hz. Assume the speed of sound in the air 340m/s. The length of the organ pipe is?

What is open organ pipe? It means two open ends? Like this? Or one closed and one open?

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Should I use this formula? $L=\frac{(2n+1)v}{4f}$


1 Answer 1


Open organ pipe is the one with two open ends, and instead of the formula you mention you need to use $$L=n\frac{v}{2f_n}$$ where $f_n$ is the frequency of the ${n^{th}}$ mode, and $n=1,2,3,...$ your formula is for a closed organ pipe (with one open and one closed end).


Because the number of half-wavelengths ($\lambda /2$) need to be an integral multiple in case of a open pipe. This is because both the ends of an open organ pipe are pressure nodes (or displacement antinodes), and the difference between two successive nodes (or antinodes) is $\frac{\lambda}{2}$. Therefore, to meet the resonance-condition, the number of half wavelengths between the ends need to be an integral value, therefore $L=n\frac{v}{2f_n}$ as $v=f\lambda$.

  • $\begingroup$ Sorry, I do not understand. For two open end, why not $L=\frac{nv}{2f}+\frac{v}{2f}=\left(\frac{n}{2}+\frac{1}{2}\right)\left(\frac{v}{f}\right)=\left(\frac{n+1}{2}\right)\left(\frac{v}{f}\right)$? Thank you for explaination. $\endgroup$
    – Casper
    Oct 19, 2013 at 9:48
  • $\begingroup$ @CasperLi See the edit in my answer $\endgroup$ Oct 19, 2013 at 12:35

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