Two open organ pipes of fundamental frequencies n₁ and n₂ are joined in series. fundamenta

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14.Waves and Sound

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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

$n_1 + n_2$

$n_1n_2 / (n_1 + n_2)$

$\sqrt {n_1n_2}$

$\sqrt {(n^2_1 + n^2_2)}$

Solution

$n_{1}=\frac{V}{2 \ell_{1}}, n_{2}=\frac{V}{2 \ell_{2}}$

When joined in series $\ell=\ell_{1}+\ell_{2}$

$n=\frac{V}{2 \ell}=\frac{V}{2\left(\ell_{1}+\ell_{2}\right)}=\frac{V}{2\left(\frac{V}{2 n_{1}}+\frac{V}{2 n_{2}}\right)}=\frac{n_{1} n_{2}}{n_{1}+n_{2}}$

Standard 11

Physics

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normal

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

Solution

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