Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies ' n₁ ', and ' n₂ ' respectively. When both pipes are joined to form a single pipe, its fundamental frequency will be (a) (n₁ + n₂)/(n₁ n₂) (b) (n₁ n₂)/(2n₂ + n₁) (c) (2n₂ + n₁)/(n₁ n₂) (d) (n₁ n₂)/(n₁ + n₂)

Answer: (d). Open pipe fundamental: n = v/2L ⇒ L = v/2n L₁ = v/2n₁, L₂ = v/2n₂; joined pipe has L = L₁ + L₂ = v/2(1/n₁ + 1/n₂) n = v/2L = (1)/(1/n₁ + 1/n₂) = (n₁ n₂)/(n₁ + n₂) So the answer is (d) (n₁ n₂)/(n₁ + n₂).

Two open pipes of different lengths and same diameter in which the… | MHT CET 2019 (2 May, Shift 1)

Q104MHT CET 2019 · 2 MAY · SHIFT 1Medium

Organ Pipes & Resonance Tube

Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies ' $n_1$ ', and ' $n_2$ ' respectively. When both pipes are joined to form a single pipe, its fundamental frequency will be

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Answer: (d)

Open pipe fundamental: $n = \frac{v}{2L} \Rightarrow L = \frac{v}{2n}$
$L_1 = \frac{v}{2n_1}$ , $L_2 = \frac{v}{2n_2}$ ; joined pipe has $L = L_1 + L_2 = \frac{v}{2}\left(\frac{1}{n_1} + \frac{1}{n_2}\right)$
$n = \frac{v}{2L} = \frac{1}{\frac{1}{n_1} + \frac{1}{n_2}} = \frac{n_1 n_2}{n_1 + n_2}$
So the answer is (d) $\frac{n_1 n_2}{n_1 + n_2}$ .

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Organ Pipes & Resonance Tube question from MHT CET 2019 (2 May, Shift 1)

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