Standing Waves in Open Organ Pipe

Q. A tube $1.20\text{m}$ long is closed at one end. A stretched wire is placed near the open end. The wire is $0.330\text{m}$ long and has a mass of $9.60\text{g}$. It is fixed at both ends and oscillates in its fundamental mode. By resonance, it sets the air column in the tube into oscillation at the fundamental frequency. Then:
[Take speed of sound in air as $343\text{m/s}$]

1. Fundamental frequency of air column is $71.45\text{Hz}$.
2. Fundamental frequency of air column is $35\text{Hz}$.
3. The tension in the wire is $29.5\text{N}$.
4. The tension in the wire is $64.50\text{N}$.

Q. The air column in an open organ pipe is made to vibrate in its first overtone by a tuning fork of frequency $680\text{Hz}$. Speed of sound in air is $340\text{m/s}$ and ${10}^5{\text{N/m}}^2$ is the mean pressure at any point in the pipe. If $10{\text{N/m}}^2$ is the maximum amplitude of pressure variation, then

1. Length of organ pipe is $1\text{m}$.
2. Amplitude of pressure variation at $x=\frac{1}{3}$ is $8.6{\text{N/m}}^2$.
3. Pressure at the end of the pipe is ${10}^5{\text{N/m}}^2$.
4. Maximum pressure in the pipe is $({10}^5+10){\text{N/m}}^2$.

Q. The velocity of sound in air is $333\text{m/s}$. In order to produce the second overtone of frequency $999\text{Hz}$ in it, the length of the open organ pipe will be :

1. $0.5\text{m}$
2. $1\text{m}$
3. $1.5\text{m}$
4. $0.25\text{m}$

Q. The vibration of air in an open organ pipe of length $30\text{cm}$ is represented by $\Delta p=8\sin \left(\frac{2\pi x}{25}\right)\cos \left(48\pi t\right),$ where $x,p\text{and}t$ are in $\text{cm},{\text{N/m}}^2$ and $\text{sec}$ respectively. The excess pressure (pressure over atmospheric pressure) amplitude at $x=10\text{cm}$ is
[ Take $\sin \left(\frac{4\pi }{5}\right)=0.587$ ]

1. $5{\text{N/m}}^2$
2. $4{\text{N/m}}^2$
3. $4.5{\text{N/m}}^2$
4. $4.7{\text{N/m}}^2$

Q. The fundamental frequency of an open organ pipe is equal to the second overtone of a closed organ pipe. If the length of closed organ pipe is $40\text{cm}$, the length of open organ pipe is

1. $13.3\text{cm}$
2. $8\text{cm}$
3. $12.5\text{cm}$
4. $16\text{cm}$

Q. In a closed organ pipe of length $105\text{cm}$, standing waves are set up corresponding to the third overtone. At what minimum distance from the closed end a pressure node is formed?

1. $18\text{cm}$
2. $15\text{cm}$
3. $25\text{cm}$
4. $30\text{cm}$

Q. An open pipe vibrating in its fundamental frequency is suddenly closed at one end. As a result, the frequency of the third harmonic of the closed pipe is found to be higher by $100\text{Hz}$. The fundamental frequency of the open pipe is :-

1. $200\text{Hz}$
2. $30\text{Hz}$
3. $240\text{Hz}$
4. $480\text{Hz}$

Q. The equation of a standing wave in an open organ pipe is given by: $p=16\sin \left(\frac{\pi }{3}x\right)\cos \left(64t\right)$, where symbols have their usual meaning. Here $x$ is in $\text{cm}$, $t$ is in $\text{seconds}$ and the amplitude is given in $\text{cm}$ .Then, the first pressure node is obtained at a distance $x$ from one end. What is the value of $x$?

1. $2\text{cm}$
2. $3\text{cm}$
3. $4\text{cm}$
4. $5\text{cm}$

Q.

A closed organ pipe can vibrate at a minimum frequency of 500 Hz. Find the length of the tube. Speed of sound in air = $340m{s}^{-1}$.

1. 8.5 cm

2. 17 cm

3. 34 cm

4. None of these

Q. A longitudinal sound wave given by $p=5\sin \frac{\pi }{3}(x-400t)$ ($p$ is in ${\text{N/m}}^2$, $x$ is in metres and $t$ is in seconds) is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is

1. $7.5\text{m}$
2. $15\text{m}$
3. $5\text{m}$
4. $2\text{m}$

Q. An air column closed at one end and open at the other end resonates with a tuning fork when the length of the column is smallest and equal to $50\text{cm}$. The next larger length of column resonating with same tuning fork is

1. $100\text{cm}$
2. $125\text{cm}$
3. $175\text{cm}$
4. $150\text{cm}$

Q. A closed organ pipe of length $100\text{cm}$ and an open organ pipe contain gases of densities $9{\text{kg/m}}^3$ and $1{\text{kg/m}}^3$, respectively. The compressibility of gases is equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open organ pipe is $\text{(in m)}$

Q. An open organ pipe has a length of $10\text{cm}$ . If the speed of sound in air is $340\text{m/s}$ and the audible range is $(20-20,000\text{Hz})$, then choose the correct option(s):

1. The fundamental frequency of vibration of this pipe is $1700\text{Hz}$.
2. $11$ is the highest harmonic of such tube in audible range.
3. $6800\text{Hz}$ is the third overtone frequency.
4. The fundamental frequency of vibration of this pipe is $1200\text{Hz}$.

Q. An open pipe vibrating in its fundamental frequency is suddenly closed at one end. As a result, the frequency of the third harmonic of the closed pipe is found to be higher by $100\text{Hz}$. The fundamental frequency of the open pipe is :-

1. $200\text{Hz}$
2. $30\text{Hz}$
3. $240\text{Hz}$
4. $480\text{Hz}$

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

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

Q. A cylindrical metal tube has a length of $50\text{cm}$ and is open at both ends. Find the frequencies between $1\text{kHz}$ to $2\text{kHz}$ at which the air column in the tube resonates. The temperature on that day is ${20}^{\circ }C$.
[Take $v_0=330\text{m/s}$]

1. $1020,11360,1700\text{Hz}$
2. $1026,1368,1710\text{Hz}$
3. $1328,1660,1922\text{Hz}$
4. None of these

Q. Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the range $(40-20000\text{Hz})$
[Assume, speed of sound in air = $340{\text{ms}}^{-1}$]

1. $8.5\text{cm}$
2. $4.25\text{cm}$
3. $4.5\text{cm}$
4. $2.25\text{cm}$

Q.

A closed organ pipe can vibrate at a minimum frequency of 500 Hz. Find the length of the tube. Speed of sound in air = $340m{s}^{-1}$.

1. 8.5 cm

2. 17 cm

3. 34 cm

4. None of these