Standing Waves in Closed Organ Pipe

Q.

A closed pipe and an open pipe have their first overtones identical in

frequency. Their lengths are in the ratio

[Roorkee 1999]

1. 1 : 2

2. 2 : 3

3. 3 : 4

4. 4 : 5

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.

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is:

1. 300 Hz

2. 200 Hz

3. 240 Hz

4. 480 Hz

Q. A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source ? Will the same source be in resonance with the pipe if both ends are open? (speed of sound in air is 340 m s¯¹).

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

Q.

Find the fundamental, first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is 340$m{s}^{-1}$.

1. 120, 240 360 Hz

2. 850 Hz, 1750 Hz, 2550 Hz

3. 150, 300 450 Hz

4. None of these

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. 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. 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.

You have a test tube of length 14 cm. You blow in it and form standing waves. Can you tell the fundamental frequency of standing wave formed in the tube if it was half filled with ice. (i) for diagram 1 (ii) for diagram 2

Given v = 336 $\frac{m}{s}$

1. (i) - 600 Hz (ii) - 800 Hz

2. (i) - 1200 Hz (ii) 600 Hz

3. (i) - 800 Hz (ii) - 1200 Hz

4. (i) - 600 Hz (ii) - 600 Hz

Q. A tuning fork of frequency $300\text{Hz}$ is vibrated on arm-$1$, then the air column vibrates in fundamental mode. If the same tuning fork is vibrated on arm-$2$, the air column vibrates in first overtone. Both the arms are of length $1\text{m}$. If velocity of sound is $300\text{m/s},g=10{\text{m/s}}^2$ and density of water is ${10}^3{\text{kg/m}}^3$ then the density of the unknown liquid is
$($Neglect surface tension and end corrections$)$

1. $2\times {10}^3{\text{kg/m}}^3$
2. $4\times {10}^3{\text{kg/m}}^3$
3. $3\times {10}^3{\text{kg/m}}^3$
4. $5\times {10}^3{\text{kg/m}}^3$

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.

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. How many harmonics in the audible range are present in the vibrations of air column in a closed organ pipe of length 0.2m. Given velocity of sound $=340m{s}^{-1}$

1. 12
2. 18
3. 24
4. 30

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 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 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.

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is:

1. 200 Hz

2. 300 Hz

3. 240 Hz

4. 480 Hz

Q.

You have 2 pipes of length 1.20 m. One pipe is open, other has one end closed. First overtone is formed in both the pipes. Find the position of 1^st displacement node from origin

1. 0.6 m, 0.6 m

2. 0.4 m, 0.3 m

3. 0.3 m, 0.4 m

4. 0.6 m, 0.8 m

Q. A tuning fork vibrates at $260\text{Hz}$. Find the length of the shortest closed organ pipe that will resonate with the tuning fork. Given, speed of sound in air is $340\text{m/s}$.

1. $30\text{cm}$
2. $3.8\text{cm}$
3. $33\text{cm}$
4. $44\text{cm}$