MCQ
The number of possible natural oscillations of air column in a pipe closed at one end of length $85 \,\,cm$ whose frequencies lie below $1250\,\, Hz$ are (Velocity of sound $= 340 \,\,m s^{-1}$)
- A$4$
- B$5$
- ✓$6$
- D$7$
✓
Answer
Correct option: C.
$6$
c
Fundamental frequency of the closed organ pipe is
Fundamental frequency of the closed organ pipe is
$v=\frac{v}{4 L}$
Here, $v=340 \mathrm{m} \mathrm{s}^{-1}, L=85 \mathrm{cm}=0.85 \mathrm{m}$
$\therefore \quad v=\frac{340 \mathrm{ms}^{-1}}{4 \times 0.85 \mathrm{m}}=100 \mathrm{Hz}$
The natural frequencies of the closed organ pipe will be
$v_{n} =(2 n-1) v=v, 3 v, 5 v, 7 v, 9 v, 11 v, 13 v, \ldots$
$=100 \mathrm{Hz}, 300 \mathrm{Hz}, 500 \mathrm{Hz}, 700 \mathrm{Hz}, 900 \mathrm{Hz}$
$1100 \mathrm{Hz}, 1300 \mathrm{Hz}, \ldots$ and so on
Thus, the natural frequencies lies below the $1250 \mathrm{Hz}$ is $6.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Four point masses, each of value $m$, are placed at the comers of a square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is
→A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t,$ and another plate $Y$ of radius $4R$ is made from an iron plate of thickness $\frac{\text{t}}{4}$ The ratio between moment of inertia $\frac{\text{I}_{\text{y}}}{\text{I}_{\text{x}}}$ is:
→Steam at $100^o C$ is added slowly to $1400 \,\,gm$ of water at $16^o C$ until the temperature of water is raised to $80^o C$. The mass of steam required to do this is ($L_V =$ $540\,\,cal/gm$) ........... $gm$
→A ball attached to one end of a string swings in a vertical plane such that its acceleration at point $A$ (extreme position) is equal to its acceleration at point $B$ (mean position). The angle $\theta$ is :-
→For inelastic collision between two spherical rigid bodies
If a body is charged by rubbing it, its weight
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it.
A body is moving under the action of two forces ${\vec F_1} = 2\hat i - 5\hat j\,;\,{\vec F_2} = 3\hat i - 4\hat j$. Its velocity will become uniform under an additional third force ${\vec F_3}$ given by
→A body of $10\, kg$ is acted by a force of $129.4\, N$ if $g = 9.8\,m/{\sec ^2}$. The acceleration of the block is $10\,m/{s^2}$. What is the coefficient of kinetic friction
→A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is $T_0$. What must be the acceleration of the lift for the period of oscillation of the pendulum to be $T_0/2$ ?
→