Standing Waves in Closed Organ Pipe

Q. The two nearest harmonics of a tube closed at one end and open at the other end are $220\text{Hz}$ and $260\text{Hz}$. What is the fundamental frequency of the system?

1. $20\text{Hz}$
2. $30\text{Hz}$
3. $40\text{Hz}$
4. $10\text{Hz}$

Q. The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of open organ pipe is $80\text{cm}$ then the length of the closed organ pipe will be

1. $30\text{cm}$
2. $35\text{cm}$
3. $40\text{cm}$
4. $20\text{cm}$

Q. An organ pipe closed at one end has a fundamental frequency of $1500\text{Hz}$. The maximum number of overtones generated by this pipe which a normal person can hear is

1. $6$
2. $7$
3. $14$
4. $13$

Q. An open organ pipe has fundamental frequency of $300\text{Hz}$. The first overtone of this organ pipe is same as the first overtone of a closed organ pipe. Find the length of the closed organ pipe?
[speed of sound in air $=330\text{m/s}$]

1. $45\text{cm}$
2. $41\text{cm}$
3. $42\text{cm}$
4. $48\text{cm}$

Q. An organ pipe $P_1$ closed at one end is vibrating in its first overtone and another organ pipe $P_2$ opened at both ends is vibrating in its third overtone are in resonance with a given tuning fork. The ratio of length of organ pipe $P_1$ and $P_2$ is

1. $\frac{2}{3}$
2. $\frac{1}{3}$
3. $\frac{3}{8}$
4. $\frac{8}{3}$

Q. The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies $f_p:f_q:f_r:f_s$ will be

1. $1:2:4:3$
2. $4:2:3:1$
3. $6:2:3:4$
4. $1:1:1:1$

Q. The third harmonic of a closed organ pipe is equal to the second overtone of an open organ pipe. If the length of open organ pipe is $60\text{cm}$, then the length of closed organ pipe will be

1. $20\text{cm}$
2. $40\text{cm}$
3. $30\text{cm}$
4. $50\text{cm}$

Q.

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2m{s}^{-1}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320m{s}^{-1}$, the smallest value of the percentage change required in the length of the pipe is ____________.

Q. A closed organ pipe of length $10\text{cm}$ has fundamental frequency equal to half the value of the second overtone of an open organ pipe. The length of the open organ pipe will be

1. $10\text{cm}$
2. $20\text{cm}$
3. $30\text{cm}$
4. $40\text{cm}$

Q. A cylindrical tube open at both ends has a fundamental frequency $f$ in air. The tube is dipped vertically in water so that it has water up to the half height. The fundamental frequency of the air column is now
(Neglect end corrections)

1. $4f$
2. $f$
3. $3f$
4. $2f$

Q.

A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.

Q.

In $1m$ long open pipe, what is the harmonic of resonance obtained with a tuning fork of frequency $480Hz$?

1. First

2. Second

3. Third

4. Fourth

Q. The activity of a freshly prepared radioactive sample is ${10}^{10}$ disintegrations per second, whose mean life is ${10}^{9}s$. The mass of an atom of this radioisotope is ${10}^{-25}kg.$ The mass $\left(inmg\right)$ of the radioactive sample is

Q. The first overtone frequency of a closed organ pipe $P_1$ is equal to the fundamental frequency of an open organ pipe $P_2$. If the length of the pipe $P_1$ is $60\text{cm}$, what will be the length of $P_2$?

1. $20\text{cm}$
2. $60\text{cm}$
3. $80\text{cm}$
4. $40\text{cm}$

Q. A tuning fork vibrates at $250\text{Hz}$. Find the length of the shortest closed organ pipe that will resonate with the tuning fork.
[Speed of sound in air $=340\text{m/s}$]

1. $35\text{cm}$
2. $33\text{cm}$
3. $34\text{cm}$
4. $36\text{cm}$

Q. For a certain organ pipe, three successive resonance frequencies are observed at $425\text{Hz}$, $595\text{Hz}$ and $765\text{Hz}$ respectively. The fundamental frequency of the pipe is -
$[$speed of sound in air $=340\text{m/s}]$

1. $85\text{Hz}$
2. $45\text{Hz}$
3. $25\text{Hz}$
4. $70\text{Hz}$

Q. A tuning fork vibrates at $264\text{Hz}$. The shortest length of a closed organ pipe that will resonate with the tuning fork is
[Speed of sound in air $=350\text{m/s}$]

1. $65\text{cm}$
2. $95\text{cm}$
3. $33\text{cm}$
4. $75\text{cm}$

Q. In the circuit shown $R_1=R_2=10\Omega$ and resistance per unit length of wire PQ = $1\Omega$/cm and length PQ = 10 cm. If $R_2$ is made $20\Omega$ then to get zero deflection in galvanometer. S is midpoint of wire PQ:-

1. The jockey at P can be moved towards right 2 cm
2. The jockey at Q can be moved towards left 2 cm
3. The jockey at S can be moved towards left a distance $\frac{5}{3}m$
4. The jockey at all position fixed and $R_1$ should be made 20$\Omega$

Q.

If the length of an open organ pipe is 33.3 cm, then the frequency of fifth overtone is: $(V_{sound}=333m/s)$

1. 2500 Hz

2. 1250 Hz

3. 1500 Hz

4. 3000 Hz

Q.

A 2.00 m - long rope, having a mass of 80 g, is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N. (a) Find the frequencies of the fundamental and the first two overtones. (b) Find the wavelength in the fundamental and the first two overtones.

Q. The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metres long. The length of the open pipe will be

1. $4L$
2. $L$
3. $2L$
4. $\frac{L}{2}$

Q. A human body excretes (removes by waste discharge, sweating etc) certain materials by a law similar to radioactivity. If technetium is injected in some form in a human body, the body excretes half the amount in $24$ hours. A patient is given an injection containing ${}^{99}\text{Tc}$. This isotope is radioactive with a half-life of $6$ hours. The activity from the body just after the injection is $6\mu \text{Ci}$. How much time will elapse before the activity falls to $3\mu \text{Ci}$ ?

1. $24\text{hours}$
2. $6.4\text{hours}$
3. $4.8\text{hours}$
4. $2\text{hours}$

Q. $n^{th}$ harmonic of a closed organ pipe is equal to $m^{th}$ harmonic of an open pipe. First overtone frequency of the closed organ pipe is also equal to first overtone frequency of the open organ pipe. Find the value of n if m = 6? ___

Q. A tube of length $1\text{m}$ containing $H_2$ is closed at one end. If the velocity of sound in air be $340\text{m/s}$. Then, the fundamental frequency and the next higher overtone in $H_2$ are:

1. $85\text{Hz},170\text{Hz}$
2. $170\text{Hz},255\text{Hz}$
3. $85\text{Hz},255\text{Hz}$
4. $55\text{Hz},255\text{Hz}$

Q. An air column is constructed by fitting a movable piston in a long cylindrical tube. Longitudinal waves are sent in the tube by a tuning fork of frequency $416\text{Hz}$. How far from the open end should the piston be so that the air column in the tube may vibrate in its first overtone neglecting the end corrections?
$[$ speed of sound in air $=333\text{m/s}]$

1. $30\text{cm}$
2. $45\text{cm}$
3. $60\text{cm}$
4. $90\text{cm}$

Q. The third overtone of a closed pipe differs by $200H_Z$ from the first overtone of an open pipe what is the fundamental frequency of the closed pipe? Given length of the two pipes are l

1. 50 Hz
2. 60 Hz
3. 40 Hz
4. 70 Hz

Q. The pressure wave in a closed organ pipe of length $40\text{cm}$ is given by $p=5\sin \left(\frac{2\pi x}{32}\right)\cos \left(50\pi t\right)$ where $x,p$ and $t$ are in $\text{cm},{\text{N/m}}^2$ and seconds respectively. The pressure nodes are located at which of the following distances along the pipe (from the open end) ?

1. $8\text{cm},24\text{cm}$
2. $16\text{cm},32\text{cm}$
3. $16\text{cm},24\text{cm}$
4. $18\text{cm},32\text{cm}$

Q. Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube A and B is

1. 4 : 1
2. 1 : 2
3. 1 : 4
4. 2 : 1

Q. A pipe closed at one end produces a fundamental frequency of $375\text{Hz}$. If it is cut into two pipes of equal length, then the fundamental frequency produced by the open and closed pipes respectively are

1. $375\text{Hz},750\text{Hz}$
2. $1500\text{Hz},750\text{Hz}$
3. $750\text{Hz},1000\text{Hz}$
4. $750\text{Hz},750\text{Hz}$

Q. The number of possible modes of natural oscillations of air column in a pipe closed at one end of length $170\text{cm}$ below frequency $1450\text{Hz}$ are
[velocity of sound $=340{\text{ms}}^{-1}$]

1. $14$
2. $13$
3. $12$
4. $15$