Two open organ pipes of fundamental frequenci | vedclass

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(C) The fundamental frequency of an open organ pipe of length $L$ is given by $n = \frac{v}{2L}$,where $v$ is the speed of sound.From this,the length

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$\frac{n_{1}n_{2}}{n_{1} + n_{2}}$

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(C) The fundamental frequency of an open organ pipe of length $L$ is given by $n = \frac{v}{2L}$,where $v$ is the speed of sound.From this,the length of the pipe is $L = \frac{v}{2n}$.For the two pipes with fundamental frequencies $n_{1}$ and $n_{2}$,their lengths are $L_{1} = \frac{v}{2n_{1}}$ and $L_{2} = \frac{v}{2n_{2}}$.When these two pipes are joined in series,the total length of the new pipe becomes $L_{new} = L_{1} + L_{2}$.The fundamental frequency $n$ of the new pipe is $n = \frac{v}{2L_{new}} = \frac{v}{2(L_{1} + L_{2})}$.Substituting the values of $L_{1}$ and $L_{2}$:$n = \frac{v}{2(\frac{v}{2n_{1}} + \frac{v}{2n_{2}})} = \frac{v}{v(\frac{1}{n_{1}} + \frac{1}{n_{2}})} = \frac{1}{\frac{n_{1} + n_{2}}{n_{1}n_{2}}}$.Therefore,$n = \frac{n_{1}n_{2}}{n_{1} + n_{2}}$.

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained will be

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