Standing Waves in Closed Organ Pipe

Q. An air column vibrates in a pipe closed at one end in its third overtone due to a tuning fork of frequency $595\text{Hz}$. $P_o$ is the mean pressure at any point in the pipe and $\Delta P_o$ is the maximum amplitude of pressure variation. Speed of sound in air is $340\text{m/s}$ and end correction has a negligible effect. If the amplitude of pressure variation at the middle of the pipe is $\frac{\Delta P_o}{\sqrt{n}},$ then $n$ is:
[Given $\cos \left(\frac{595\pi }{340}\right)=\frac{1}{\sqrt{2}}$ ]

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

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

Q. The first overtone frequency of a closed organ pipe is equal to the second overtone frequency of an open organ pipe. If the length of the open pipe is $80\text{cm}$, what is the length of the closed organ pipe?

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

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

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

Q. A tube open at only one end is cut into two tubes of non-equal lengths. The piece open at both the ends has a fundamental frequency of $450\text{Hz}$ and the other piece has a fundamental frequency of $675\text{Hz}$. What is the first overtone frequency of the original tube?

1. $506.25\text{Hz}$
2. $606.25\text{Hz}$
3. $406.25\text{Hz}$
4. $306.25\text{Hz}$

Q. A closed organ pipe of length $l$ is vibrating in $3^{rd}$ overtone with amplitude of antinode being ${}^{\prime }{a}^{\prime }$. Amplitude at a distance $\frac{l}{7}$ from the closed end is

1. $\frac{a}{2}$
2. $a$
3. $\frac{\sqrt{3}a}{2}$
4. $\text{None}$

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

Q. The first overtone frequency of a closed organ pipe is equal to the second overtone frequency of an open organ pipe. If the length of the open pipe is $80\text{cm}$, what is the length of the closed organ pipe?

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

Q. A $50\text{cm}$ long wire having a mass of $20\text{g}$ is fixed at two ends and is vibrated in its fundamental mode. A $75\text{cm}$ long closed organ pipe, placed with its open end near the wire, is set up into resonance in its first overtone mode by the vibrating wire. Find the tension in the wire. Speed of sound in air is $340\text{m/s}$.

1. $2446\text{N}$
2. $4264\text{N}$
3. $4624\text{N}$
4. $4552\text{N}$

Q. A closed organ pipe of length $l$ is vibrating in $3^{rd}$ overtone with amplitude of antinode being ${}^{\prime }{a}^{\prime }$. Amplitude at a distance $\frac{l}{7}$ from the closed end is

1. $\frac{a}{2}$
2. $a$
3. $\frac{\sqrt{3}a}{2}$
4. $\text{None}$

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

Q. A $50\text{cm}$ long wire having a mass of $20\text{g}$ is fixed at two ends and is vibrated in its fundamental mode. A $75\text{cm}$ long closed organ pipe, placed with its open end near the wire, is set up into resonance in its first overtone mode by the vibrating wire. Find the tension in the wire. Speed of sound in air is $340\text{m/s}$.

1. $2446\text{N}$
2. $4264\text{N}$
3. $4624\text{N}$
4. $4552\text{N}$

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

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

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

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. $15$

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

Q. The two nearest harmonics of a tube closed at one end and open at the other end are $220\text{Hz}$ and $240\text{Hz}$ respectively. What is the fundamental frequency of the system?

1. $10\text{Hz}$
2. $20\text{Hz}$
3. $30\text{Hz}$
4. $15\text{Hz}$

Q.

A closed pipe has length 0.6m. The air inside the pipe is maintained at temperature ${27}^{\circ }C$. Calculate the fundamental frequency and the frequency of the next two overtones.
(given velocity of sound in air at $0^{\circ }C=330m{s}^{-1}$)

1. 144 Hz, 288 Hz, 432 Hz

2. 144 Hz, 432 Hz, 720 Hz

3. 144 Hz, 216 Hz, 288 Hz

4. None of these

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

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