Standing Waves in Open Organ Pipe

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

Q.

A student is performing the experiment of resonance column. The diameter of the column tube is $6cm$. The frequency of the tuning fork is $504Hz$. Speed of the sound at the given temperature is $336m{s}^{-1}$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

1. $13cm$

2. $14.8cm$

3. $16.6cm$

4. $18.4cm$

Q.

How is the frequency of a stretched string related to its tension?

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. Third overtone of a closed organ pipe is equal to the second harmonic of an open organ pipe. Then the ratio of their length is equal

1. $\left(\frac{12}{11}\right)$
2. $\left(\frac{4}{7}\right)$
3. $\left(\frac{7}{4}\right)$
4. $\left(\frac{11}{12}\right)$

Q. A vibrating tuning fork generates a wave given by $y=0.1\sin \pi (0.1x-2t)$ where $x$ and $y$ are in $\text{metre}$ and time $t$ in $\text{second}$. The distance travelled by the wave while the fork completes $25$ vibrations is

1. $250\text{m}$
2. $500\text{m}$
3. $750\text{m}$
4. $1000\text{m}$

Q.

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by

$y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right].$

(a) What is the frequency of vibration ? (b) What are the positions of the nodes? (c) What is the length of the string ? (d) What is the waavelength and the speed of two travelling waves that can interfere to give this vibration ?

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.

In a resonance column experiment, a tuning fork of frequency 400 Hz is used. The first resonance is observed when the air column has a length of 20.0 cm and the second resonance is observed when the air column has a length of 62.0 cm. (a) Find the speed of sound in air. (b) How much distance above the open end does the , pressure node form ?

Q. Two successive resonance frequencies in an open organ pipe are $1954\text{Hz}$ and $2602\text{Hz}$. Find the length of the tube.
[Given, speed of sound in air is $324{\text{ms}}^{-1}$]

1. $25\text{cm}$
2. $50\text{cm}$
3. $75\text{cm}$
4. $100\text{cm}$

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.

In a resonance tube experiment when the tube is filled with water up to a height of $17.0cm$ from the bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5cm$. If the velocity of sound in air is $330m/s$, the tuning fork frequency is:

1. $2200Hz$

2. $550Hz$

3. $3300Hz$

4. $1100Hz$

Q.

What are the different types of harmonics?

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. chlorine
3. hydrogen
4. oxygen

Q.

Consider the situation shown in figure (16-E9). The wire which has a mass of 4.00 g oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode. Assuming that the speed of sound in air is $340m{s}^{-1}$, find the tension in the wire.

Q.

Figure (15-E7) shows two wave pulses at t = 0 travelling on a string in opposite directions with the same wave

speed $50cm{s}^{-1}.$ Sketch the shape of the string at t = 4 ms, 6 ms, 8 ms, and 12 ms.

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

Q. A tuning fork of frequency $330\text{Hz}$ is vibrated just above the tube of $100\text{cm}$ height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance?

$[$Take speed of sound $=330\text{m/s}]$

1. $40\text{cm}$
2. $35\text{cm}$
3. $30\text{cm}$
4. $25\text{cm}$

Q. If the temperature of air in an organ pipe increases, what happens to the resonance frequencies ?

1. Remains same
2. Decreases
3. Depends on density of air
4. Increases

Q. Velocity of sound in air is $320\text{m/s}$. A pipe closed at one end has a length of $1\text{m}$, neglecting end corrections. Find the frequency(s) for which the air column in the pipe can resonate.

1. $80\text{Hz}$
2. $240\text{Hz}$
3. $500\text{Hz}$
4. $400\text{Hz}$

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. The two nearest harmonics of a tube closed at one end and open at other end are $220Hz$ and $260Hz$. What is the fundamental frequency of the system ?

1. $40Hz$
2. $10Hz$
3. $20Hz$
4. $30Hz$

Q. The pitch of an organ pipe vibrating in a certain mode for a given temperature is highest when the pipe is filled with

1. Nitrogen
2. Hydrogen
3. Oxygen
4. Fluorine

Q.

State factors on which frequency of fundamental note of a vibrating string depends.

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. In the figure the string has a mass $4.5\text{g}$. How much time will it take for a transverse disturbance produced at the floor to reach the pulley ?
(Take $g=10{\text{ms}}^{-2}$ and assume that tension in the string is constant throughout)

1. $0.04\text{s}$
2. $0.2\text{s}$
3. $0.4\text{s}$
4. $0.02\text{s}$

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. For a certain organ pipe, three successive resonance, frequencies are observed at $425,595$ and $765Hz$ respectively. Taking the speed of sound in air to be $340m/s$ the fundamental frequency of the pipe (in Hz) is

1. $425$
2. $170$
3. $85$
4. $245$

Q.

The frequency of the first harmonic produced in air column enclosed in a closed pipe is 300 Hz. If its length is 40 cm, then what is the velocity of the sound in air?

1. 320 m s^-1

2. 340 m s^-1

3. 400 m s^-1

4. 480 m s^-1