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 $2 {cm}^{2},$ the amount of water poured in the organ tube is _______ g. (Take speed of sound in air is 330 m/s)

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answer is 400.

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Detailed Solution

$\frac{V}{4 ℓ_{1}} = 30 \Rightarrow ℓ_{1} = \frac{11}{4} m$

$\frac{V}{4 ℓ_{2}} = 110 \Rightarrow ℓ_{2} = \frac{3}{4} m$

$Δℓ = 2 m$

Change in volume $= AΔℓ = 400 {cm}^{3}$

$M = 400 g; (∵ ρ = 1 g / {cm}^{3})$

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