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If ' $l$ ' is the length of the open pipe, ' $r$ ' is the internal radius of the pipe and ' $V$ ' is the velocity of sound in air then fundamental frequency of open pipe is
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Verified Answer
The correct answer is:
$\frac{\mathrm{V}}{2(l+1.2 \mathrm{r})}$
For an open organ pipe, the length of the pipe with end correction is given as:
$$
\begin{aligned}
& \mathrm{L}=l+2 \mathrm{e}=l+2 \times 0.6 \mathrm{r} \\
& \mathrm{L}=l+1.2 \mathrm{r}
\end{aligned}
$$
$\therefore \quad$ The fundamental frequency of open pipe is:
$$
\begin{aligned}
& \mathrm{f}=\frac{\mathrm{v}}{2 \mathrm{~L}} \\
& \mathrm{f}=\frac{\mathrm{v}}{2(l+1.2 \mathrm{r})}
\end{aligned}
$$
$$
\begin{aligned}
& \mathrm{L}=l+2 \mathrm{e}=l+2 \times 0.6 \mathrm{r} \\
& \mathrm{L}=l+1.2 \mathrm{r}
\end{aligned}
$$
$\therefore \quad$ The fundamental frequency of open pipe is:
$$
\begin{aligned}
& \mathrm{f}=\frac{\mathrm{v}}{2 \mathrm{~L}} \\
& \mathrm{f}=\frac{\mathrm{v}}{2(l+1.2 \mathrm{r})}
\end{aligned}
$$
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