Standing Waves in Closed Organ Pipe

Q. A closed organ pipe of length $L$ and an open organ pipe contain gases of densities ${\rho }_1$ and ${\rho }_2$ respectively. The compressibility of the gases are equal in both the pipes. Both the pipes are vibrating in their second overtone with the same frequency. The length of the open organ pipe is:

1. $\frac{5L}{6}\sqrt{\frac{{\rho }_1}{{\rho }_2}}$
2. $\frac{5L}{6}\sqrt{\frac{{\rho }_2}{{\rho }_1}}$
3. $\frac{6L}{5}\sqrt{\frac{{\rho }_2}{{\rho }_1}}$
4. $\frac{6L}{5}\sqrt{\frac{{\rho }_1}{{\rho }_2}}$

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) - 800 Hz (ii) - 1200 Hz

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

4. (i) - 1200 Hz (ii) 600 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. 0.4 m, 0.3 m

2. 0.3 m, 0.4 m

3. 0.6 m, 0.8 m

4. 0.6 m, 0.6 m

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. None of these

3. 150, 300 450 Hz

4. 850 Hz, 1750 Hz, 2550 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. 50 Hz
2. 60 Hz
3. 40 Hz
4. 70 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. 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. 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 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. 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. $55\text{Hz},255\text{Hz}$