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)
  1. First
  2. Eighth
  3. Third
  4. 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, $\begin{aligned} v & =\mathrm{n} \frac{\mathrm{v}}{2 l_{\mathrm{o}}} \\ 2200 & =\mathrm{n}\left[\frac{330}{2 \times\left(60 \times 10^{-2}\right)}\right] \\ \therefore \quad \mathrm{n} & =\frac{2 \times\left(60 \times 10^{-2}\right) \times 2200}{330}=8 \end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 2)

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