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$A$ whistle whose air column is open at both ends has a fundamental frequency of $5100 \mathrm{Hz}$. If the speed of sound in air is $340 \mathrm{ms}^{-1}$, the length of the whistle, in $\mathrm{cm}$, is
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The correct answer is:
$10 / 3$
For an open pipe, the frequency
$$
\begin{array}{l}
f=\frac{v}{2 l} \Rightarrow 5100=\frac{340}{2 \times 1} \\
l=\frac{340}{5100 \times 2} \Rightarrow l=\frac{2}{30 \times 2}=\frac{1}{30} \mathrm{m} \\
l=\frac{100}{30}=\frac{10}{3} \mathrm{cm}
\end{array}
$$
$$
\begin{array}{l}
f=\frac{v}{2 l} \Rightarrow 5100=\frac{340}{2 \times 1} \\
l=\frac{340}{5100 \times 2} \Rightarrow l=\frac{2}{30 \times 2}=\frac{1}{30} \mathrm{m} \\
l=\frac{100}{30}=\frac{10}{3} \mathrm{cm}
\end{array}
$$
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