Standing Waves in Open Organ Pipe

Q.

Two identical flutes produce fundamental notes of frequency 300 Hz at ${27}^0$C. If the temperature of air in one flute is increased to ${31}^0$C, the number of the beats heard per second will be

1. 3

2. 4

3. 1

4. 2

Q.

A closed organ pipe and an open organ pipe are tuned to the same frequency the ratio of their length is

1. $1:1$

2. $2:1$

3. $1:4$

4. $1:2$

Q.

An open organ pipe of length L vibrates in its fundamental mode. The pressure variation is maximum

1. At distances $\frac{L}{8}$ inside from the ends.

2. At distances $\frac{L}{4}$ inside from the ends

3. At the two ends

4. At the middle of the pipe

Q.

If the length of a closed organ pipe is 1.5 m and velocity of sound is 330 m/s,

then the frequency for the second note is

[CBSE PMT 2002]

1. 165 Hz

2. 110 Hz

3. 55 Hz

4. 220 Hz

Q.

The vibration of air column in an open organ pipe of length $120\text{cm}$ is represented by $\Delta p=8\sin \left(\frac{2\pi x}{15}\right)\cos \left(48\pi t\right)$ where $x_1,\Delta p$ and $t$ are in $\text{cm}$, ${\text{N/m}}^2$ and $\text{seconds}$ respectively. Then:

1. The excess pressure amplitude at $x=2.5\text{cm}$ is $4\sqrt{3}{\text{N/m}}^2$.
2. The excess pressure amplitude at $x=2.5\text{cm}$ is $8\sqrt{3}{\text{N/m}}^2$.
3. Pressure nodes are located at $7.5\text{cm},15\text{cm},22.5\text{cm}$ from the end.
4. Pressure nodes are located at $5\text{cm},10\text{cm},15\text{cm}$ from the end.

Q.

Sounds from two identical sources $S_1$ and $S_2$ reach a point P directly in the same phase with net intensity $I_0$. The power of $S_1$ is now reduced to 64% of its initial value, and the phase difference between $S_1$ and $S_2$ is varied continuously. The maximum and minimum intensities now recorded at P are $I_{max}$ and $I_{min}$ respectively. Then

1. I_max= 0.36 I₀, I_min= 0.09 I_o

2. I_max= 0.64 I₀, I_min= 0.04 I_o

3. I_max= 0.81 I₀, I_min= 0.01 I_o

4. I_max= 1.64 I₀, I_min= 0.36 I_o

Q. A closed organ pipe, of length $1.5\text{m}$ and filled with a gas, is resonated in its fundamental mode with the help of a tuning fork. Another open pipe of same length but filled with air resonates with the same fork in its fundamental mode. The room temperature is ${30}^{\circ }\text{C}$. If the speed of sound in air at ${30}^{\circ }\text{C}$ is $340\text{m/s}$, then the speed of sound in the first gas at ${30}^{\circ }\text{C}$ will be

1. $340\text{m/s}$
2. $680\text{m/s}$
3. $510\text{m/s}$
4. $322.5\text{m/s}$

Q. Two successive resonance frequencies in an open organ pipe are $1800\text{Hz}$ and $2600\text{Hz}$. Find the length of the tube if the speed of sound in air is $340\text{m/s}$.

1. $20\text{cm}$
2. $20.5\text{cm}$
3. $21.25\text{cm}$
4. $22.25\text{cm}$

Q. The frequency of the fourth harmonic of an organ pipe is $33\text{Hz}$ less than the frequency of the fifth harmonic of the same organ pipe. Find the difference in wavelengths for the given two cases. Neglect end corrections.
[speed of sound in air $=330\text{m/s}$]

1. $60\text{cm}$
2. $50\text{cm}$
3. $40\text{cm}$
4. $30\text{cm}$

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. 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 organ pipe $\text{A}$ with both ends open, has a fundamental frequency of $300\text{Hz}$. The third harmonic of organ pipe $\text{B}$ with one end open, has the same frequency as the second harmonic of pipe $\text{A}$. What is the ratio of length of pipe $\text{A}$ to length of pipe $\text{B}$ ?

1. $\frac{2}{5}$
2. $\frac{3}{2}$
3. $\frac{4}{3}$
4. $\frac{3}{4}$

Q. A tuning fork of frequency $340\text{Hz}$ is vibrated just above a cylindrical tube. The length of the tube is $120\text{cm}$. Water is slowly poured into the tube. Determine the minimum height of water required for resonance. (Take velocity of sound in air $\text{v}=340\text{m/s}$)

1. $25\text{cm}$
2. $45\text{cm}$
3. $50\text{cm}$
4. $75\text{cm}$

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. Two successive resonance frequencies in an open organ pipe are $1944\text{Hz}$ and $2592\text{Hz}$. Find the length of the tube. The speed of sound in air is $324{\text{ms}}^{-1}$.

1. $25\text{cm}$
2. $50\text{cm}$
3. $12.5\text{cm}$
4. None of these

Q. The pitch of an open organ pipe at constant temperature corresponding to fundamental frequency is highest when the pipe is filled with

1. nitrogen
2. hydrogen
3. oxygen
4. chlorine

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. 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. Two successive resonance frequencies in an open organ pipe are $1800\text{Hz}$ and $2600\text{Hz}$. Find the length of the tube if the speed of sound in air is $340\text{m/s}$.

1. $20\text{cm}$
2. $20.5\text{cm}$
3. $21.25\text{cm}$
4. $22.25\text{cm}$

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. $5\text{cm}$