In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of 2 cm², the amount of water poured in the organ tube is __________ g. (Take speed of sound in air is 330 m/s) Numerical answer type. Work it out, then open the answer.

Answer: 400. Closed pipe fundamental: f = v/4L ⇒ L = v/4f Before: L₁ = (330)/(4 × 30) = 2.75 m; after: L₂ = (330)/(4 × 110) = 0.75 m Water column height = 2 m = 200 cm Volume = 200 × 2 = 400 cm³, mass = 400 g (density 1 g/cm³) Answer: 400 g

In a closed organ pipe, the frequency of fundamental note is 30 Hz. A… | JEE Main 2024 (30 Jan, Shift 1)

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Organ Pipes & Resonance Tube

In a closed organ pipe, the frequency of fundamental note is $30\text{ Hz}$ . A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to $110\text{ Hz}$ . If the organ pipe has a cross-sectional area of $2\text{ cm}^{2}$ , the amount of water poured in the organ tube is __________ g. (Take speed of sound in air is $330\text{ m/s}$ )

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

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Answer: 400

Closed pipe fundamental: $f = \frac{v}{4L} \Rightarrow L = \frac{v}{4f}$
Before: $L_1 = \frac{330}{4 \times 30} = 2.75\text{ m}$ ; after: $L_2 = \frac{330}{4 \times 110} = 0.75\text{ m}$
Water column height $= 2\text{ m} = 200\text{ cm}$
Volume $= 200 \times 2 = 400\text{ cm}^3$ , mass $= 400\text{ g}$ (density $1\text{ g/cm}^3$ )
Answer: $400\text{ g}$

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