End correction at open end for air column in a pipe of length ' $l$ ' is ' $e$ '. For its second overtone of…

End correction at open end for air column in a pipe of length ' $l$ ' is ' $e$ '. For its second overtone of an opern pipe, the wavelength of the wave is
  1. $\frac{2(l+\mathrm{e})}{3}$
  2. $\frac{2(l+2 \mathrm{e})}{3}$
  3. $\frac{4(l+e)}{5}$
  4. $\frac{4(l+2 \mathrm{e})}{5}$

Solution

$\begin{aligned} \therefore \quad \mathrm{n}_3 & =\frac{3 \mathrm{v}}{2 l}=\frac{3 \mathrm{v}}{2(l+2 \mathrm{e})} \\ \lambda_3 & =\frac{2(l+2 \mathrm{e})}{3} \quad \ldots .\left(\because \mathrm{v}=\mathrm{n}_3 \lambda\right)\end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 2)

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