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JEE Main 2022 (25 Jun, Shift 1) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from JEE Main 2022 (25 Jun, Shift 1)

Q76JEE Main 2022 · 25 JUN · SHIFT 1Easy

Organ Pipes & Resonance Tube

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____________ cm.

Numerical answer type. Work it out, then open the answer.

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Answer: 80

First overtone of open pipe: $\frac{v}{L_o}$ . Closed fundamental: $\frac{v}{4L_c}$ .
$\frac{v}{L_o}=\frac{v}{4L_c} \Rightarrow L_o=4L_c=4\times20$
$L_o=80\text{ cm}$

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