JEE Mains · Physics · STD 11 - Waves and sound
- JEE Mains 2025
- Medium
- MCQ
A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \(\rho_1\) and \(\rho_{2^{\prime}}\), respectively. The frequency of \(9^{\text {th }}\) harmonic of closed tube is identical with \(4^{\text {th }}\) harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is \(\rho_1: \rho_2=1: 16\), then the length of the open tube is :
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\frac{20}{9} \mathrm{~cm}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 9^{\text {th }} \text { harmonic of closed pipe }=\frac{9 \mathrm{~V}_1}{4 \ell_1} \\ & 4^{\text {th }} \text { harmonic of open pipe }=\frac{2 \mathrm{~V}_2}{\ell_2} \\ & \therefore \frac{9 \mathrm{~V}_1}{4 \ell_1}=\frac{2 \mathrm{~V}_2}{\ell_2} \\ & \therefore \frac{9}{4 \ell_1} \sqrt{\frac{\mathrm{~B}}{\rho_1}}=\frac{2}{\ell_2} \sqrt{\frac{\mathrm{~B}}{\rho_2}} \Rightarrow \frac{\ell_2}{\ell_1}=\frac{8}{9} \sqrt{\frac{\rho_1}{\rho_2}} \\ & \ell_2=\ell_1 \times \frac{8}{9} \times \frac{1}{4}=\frac{20}{9} \mathrm{~cm}\end{aligned}\)
More questions from Physics
- A gas mixture consists of \(3\,moles\) of oxygen and \(5\,moles\) or argon at temperature \(T.\) Considering only translational and rotational modes, the total internal energy of the system isJEE Mains 2019 Medium
- Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ___________ m.
\(\left( g =10 m / s ^2\right)\)JEE Mains 2026 Easy - Activities of three radioactive substances \(A , B\) and \(C\) are represented by the curves \(A, B\) and \(C,\) in the figure. Then their half-lives \(T _{\frac{1}{2}}( A ): T _{\frac{1}{2}}( B ): T _{\frac{1}{2}}( C )\) are in the ratio
JEE Mains 2020 Hard - Due to cold weather a \(1\, {m}\) water pipe of cross-sectional area \(1\, {cm}^{2}\) is filled with ice at \(-10^{\circ} {C}\). Resistive heating is used to melt the ice. Current of \(0.5\, {A}\) is passed through \(4\, {k} \Omega\) resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In \({s}\)) (Given latent heat of fusion for water/ice \(=3.33 \times 10^{5}\, {J} {kg}^{-1}\), specific heat of ice \(=2 \times 10^{3}\, {J}\) \({kg}^{-1}\) and density of ice \(=10^{3}\, {kg} / {m}^{3}\)JEE Mains 2021 Hard
- A wire of uniform resistance \(\lambda \Omega / m\) is bent into a circle of radius \(r\) and another piece of wire with length 2 r is connected between points A and B \(( AOB )\) as shown in figure. The equivalent resistance between points A and B is ___________\(\Omega\).
JEE Mains 2026 Easy - An electrical power line, having a total resistance of \(2 \Omega\), delivers \(1 \,kW\) at \(220\, V\). The efficiency of the transmission line is approximately \(.......\%\)JEE Mains 2020 Medium
More PYQs from JEE Mains
- A series \(LCR\) circuit consists of \(R =80\,\Omega X _{ L }=100\, \Omega\) and \(X _{ C }=40\, \Omega\) The input voltage is \(2500 \cos (100 \pi t )\,V\). The amplitude of current, in the circuit, is \(................A.\)JEE Mains 2023 Medium
- Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) isJEE Mains 2020 Hard