MHT CET · Physics · Waves and Sound
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)
- A First
- B Eighth
- C Third
- D Second
Answer & Solution
Correct Answer
(B) Eighth
Step-by-step Solution
Detailed explanation
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,
\(\begin{aligned}
v & =\mathrm{n} \frac{\mathrm{v}}{2 l_{\mathrm{o}}} \\
2200 & =\mathrm{n}\left[\frac{330}{2 \times\left(60 \times 10^{-2}\right)}\right] \\
\therefore \quad \mathrm{n} & =\frac{2 \times\left(60 \times 10^{-2}\right) \times 2200}{330}=8
\end{aligned}\)
\(\begin{aligned}
v & =\mathrm{n} \frac{\mathrm{v}}{2 l_{\mathrm{o}}} \\
2200 & =\mathrm{n}\left[\frac{330}{2 \times\left(60 \times 10^{-2}\right)}\right] \\
\therefore \quad \mathrm{n} & =\frac{2 \times\left(60 \times 10^{-2}\right) \times 2200}{330}=8
\end{aligned}\)
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