Q 11-14-045JEE MainJEE Main 2024 (30 Jan, Shift 1)Medium
In a closed organ pipe, the frequency of the 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 as $330\ \text{m s}^{-1}$)
Numerical value type. Enter your answer.
Answer: 400
For a closed pipe $f = \dfrac{v}{4L}$.
$$L_1 = \frac{330}{4\times30} = 2.75\ \text{m},\qquad L_2 = \frac{330}{4\times110} = 0.75\ \text{m}$$
Water column height $= 2\ \text{m} = 200\ \text{cm}$, volume $= 2\times200 = 400\ \text{cm}^3$, mass $= 400\ \text{g}$.
Solution by Sreeraj P, M.Sc Physics