Two open organ pipes of fundamental frequenci | vedclass

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(B) For an open organ pipe,the fundamental frequency is given by $n = \frac{V}{2\ell}$,where $V$ is the speed of sound and $\ell$ is the length of the

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

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(B) For an open organ pipe,the fundamental frequency is given by $n = \frac{V}{2\ell}$,where $V$ is the speed of sound and $\ell$ is the length of the pipe.For the first pipe: $\ell_{1} = \frac{V}{2n_{1}}$.For the second pipe: $\ell_{2} = \frac{V}{2n_{2}}$.When joined in series,the total length of the new pipe is $\ell = \ell_{1} + \ell_{2}$.The fundamental frequency of the new pipe is $n = \frac{V}{2\ell}$.Substituting the values of $\ell_{1}$ and $\ell_{2}$ into the equation for $\ell$:$\frac{V}{2n} = \frac{V}{2n_{1}} + \frac{V}{2n_{2}}$.Dividing both sides by $\frac{V}{2}$,we get: $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}}$.Solving for $n$: $\frac{1}{n} = \frac{n_{1} + n_{2}}{n_{1}n_{2}}$,which gives $n = \frac{n_{1}n_{2}}{n_{1} + n_{2}}$.

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

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