A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2…
A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2 KHz source?
(Speed of sound in air $=330 \mathrm{~m} / \mathrm{s})$ (Neglect end correction)
First
Eighth
Third
Second
Solution
Here, $l=60 \mathrm{~cm}, v=2200 \mathrm{~Hz}, \dot{\mathrm{v}}=330 \mathrm{~m} / \mathrm{s}$. If $\mathrm{n}^{\text {th }}$ harmonic of pipe resonates with the source, then for a open pipe,
$\begin{aligned}
v & =\mathrm{n} \frac{\mathrm{v}}{2 l_{\mathrm{o}}} \\
2200 & =\mathrm{n}\left[\frac{330}{2 \times\left(60 \times 10^{-2}\right)}\right] \\
\therefore \quad \mathrm{n} & =\frac{2 \times\left(60 \times 10^{-2}\right) \times 2200}{330}=8
\end{aligned}$