resonance tube experiment class 12

• Rotational Dynamics
• Periodic Motion
• Fluid Statics
• First Law of Thermodynamics
• Second Law of Thermodynamics
• Wave Motion
• Mechanical Waves
• Waves in Pipes and Strings
• Acoustic Phenomena
• Nature and Propagation of Light
• Interference
• Diffraction
• Polarization
• Electrical Circuits
• Thermoelectric Effects
• Magnetic Field
• Magnetic Properties of Material
• Electromagnetic Induction
• Alternating Currents
• Semiconductor Devices
• Quantization of Energy
• Radioactivity and Nuclear Reaction

1 Physics -- Waves in Pipes and Strings

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Resonance tube experiment

The experimental setup of resonance tube experiment to determine the velocity of sound in air is shown in figure.

Initially, to find the velocity of sound in air the water level in the tube is changed by changing the place of water reservoir. A tuning fork of frequency ‘f’ is set into vibration by striking it against the rubber pad and held it horizontal over the open end. The length of air column in the tube is increased by changing the position of reservoir in doing so, a condition is reached at which the sound heard is maximum, this condition is known as first resonance.

If l1 be the first resonating length and l be the wave length of sound when,

If we go on increasing the length of air column in the tube the intensity of the sound heard goes on decreasing first become minimum and then again goes on increasing at a certain length. The intensity of sound becomes maximum again, these condition is called second resonating length. If l 2  be the second resonating length,

If U be the velocity of sound at room temperature. Then,

Where f is the frequency of sound which is equal to frequency of turning fork, Velocity of sound at NTP is given by

where, P = pressure at NTP f = aqueous tension r = cubical expansively of air = 1/273

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Determining the Speed of Sound in Air in a Resonance Tube ( OCR A Level Physics )

Revision note.

Determining the Speed of Sound in Air in a Resonance Tube

Aims of the experiment.

• The aim of the experiment is calculate the speed of sound in air using a tuning fork and a tube of water
• Independent variable = Air level in the tube
• Dependent variable = Length of the air column in the tube where resonance occurs, L
• Temperature of the water
• Frequency of the tuning fork

Equipment List

Apparatus setup to measure the speed of sound in a column of air

• Set up the equipment and fill up the beaker halfway with water
• Place the tube inside the beaker, so the water comes up a quarter of the way. The side of the tube in the water acts as a closed-end
• Hold the tuning fork above the open end of the tube and strike it lightly with the small hammer
• Slowly lower the tube into the water by loosening the clamp until the intensity of sound is amplified
• When resonance (loudest sound) is heard, mark the water level with a rubber band or marker pen. Record this as L 1
• Then, lower the water further until the next point of resonance is heard and mark it. Record this as L 2
• Keep going in this manner as far as possible

Analysis of Results

• The loudness of the sound in the tube from the fork will be small at the node of the sound wave
• The sound will be the loudest at the antinode of the sound wave
• At  L 1 the wavelength is λ / 4
• At L 2 the wavelength is 3 λ / 4
• Therefore, the wavelength of the sound λ is equal to:

λ = 2(L 2 – L 1 )

• Another value of λ could also be found from the distance between  L 3 and L 2 and a mean wavelength can be calculated
• From the wave equation:
• The speed of the sound wave, v , can found from the product of the frequency f of the tuning fork and the wavelength λ calculated

Evaluating the Experiment

• The tuning fork should be struck at the same place above the tube each time
• The tuning fork should be struck with the same force each time
• Make sure the marker is a thin line to get a more accurate reading of the water level
• Submerge the tube into the water slowly, so the antinode of the sound wave (loudest sound) is not missed
• Repeat the experiment to record more reliable readings, since the point where the sound is the loudest is subjective
• Using a resonance tube with a scale will help account for error when measuring the length of the air column within it

Safety Considerations

• Don't let the tuning fork touch the tube, since the vibrations could break or crack it
• Make sure the water is at room temperature, and not too hot or cold
• Make sure no electrical equipment is near the water, otherwise they could be damaged

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Resonance Column Tube - JEE Important Topic

• Resonance Column Tube

What is a Resonance Column?

The resonance of an air column helps to determine the wavelength of the sound. The apparatus used for the experiment consists of a long cylindrical tube that is attached to the water reservoir. The resonance is indicated by the increase in the intensity of the sound.

The stationary wave is produced by the superposition of two waves of the same frequency and amplitude which are traveling with the same velocity in opposite directions. These waves produce certain fixed points along with the medium which undergoes zero displacements. These points where there is no displacement are called nodes. Somewhere, in the middle between all nodes are the regions of maximum displacement. Thus, these points are called antinodes.

Resonance Column Apparatus

The resonance air column apparatus is one of the simplest techniques used to measure the speed of sound in air at room temperature. The vibration observed in the experiment can be set up in a resonance column apparatus. This resonance is a standing wave phenomenon in the air column. The resonance column apparatus consists of a long metal tube which is held vertically in a tall jar which contains water. This tube can also be fixed in a vertical position, also the length of the column can be varied by raising or lowering the tube.

Resonance tube

Thermometer

Set Squares

Water in a beaker

Two-timing fork of known frequency

Plastic beakers

Resonance Tube Apparatus

Resonance Experiment Tube

The tube used in the experiment is filled with water. In the due course of the experiment, resonance is observed in the tube which is indicated by the sudden increase in the intensity of the sound. This resonance helps to determine the wavelength. The water level is moved up and down several times to locate the point of maximum sound intensity. The resonance counted in a certain distance of the tube is thus used to determine the wavelength and velocity of the sound. Now, let us understand the experiment a bit more clearly.

When the vibrating tuning fork is held above the open end, we can observe that longitudinal waves are sent down the air column. These waves are then reflected towards the water surface and thus produce standing waves. Here, the surface of water acts as the closed end. Also, nodes are produced at the water surface and antinodes are produced at the open end.

Waveform Construction in the Resonance Tube Experiment

Now, when the natural frequency of the tuning fork is equal to the frequency of the waves in the air column, a loud sound is produced in the column. This is the condition of resonance. This condition only occurs when the length of the air column is proportional to the one-fourth of the wavelength of the sound waves, where the frequency is equal to the frequency of tuning fork.

For first resonance,

${{l}_{1}}=\frac{\lambda }{4}$ 

Which means, for second resonance,

${{l}_{1}}=\frac{3\lambda }{4}$    

From the above both equations, we get the relation

$\lambda =2\left( {{l}_{2}}-{{l}_{1}} \right)$ 

Therefore, at room temperature, the velocity of sound in air column can be found as 

$\begin{align} & u=v\lambda  \\ & u=2v\left( {{l}_{2}}-{{l}_{1}} \right) \\  \end{align}$                                                   

The velocity of sound at ${{0}^{\circ }}C$ can be calculated as

$v=v\sqrt{\frac{273}{273+t}}$

End Correction of a Resonance Column

The short distance which is applied or added to the real length of a resonance tube, which helps to calculate the precise resonance frequency of the pipe is known as the end correction of the resonance column. A precise value of the resonance frequency is estimated when end correction is applied. It is to note that the fundamental resonance of a pipe occurs when the length of the resonator is half of the sound wavelength or quarter of the sound wavelength. The practical frequency of resonance comes out lower than this, thus we need to apply an end correction, thus the pipe used in the experiment is somewhat longer than its physical length. A precise value of resonance frequency of the pipe used in the experiment can be estimated, when an end correction is applied.

The wavelength of sound and the velocity of sound can be easily determined by the resonance tube experiment. This is based on the concept of stationary waves which get produced when two waves traveling at the same amplitude and same frequency in the opposite direction superimpose on each other. Resonance, which is a phenomenon of standing waves or stationary waves, can be used to find the velocity of sound. In order to attain an accurate value it is advisable to apply end correction to the original results.

FAQs on Resonance Column Tube - JEE Important Topic

1. Is the resonance column open pipe or closed pipe?

In the resonance column apparatus, a resonance tube is used whose one end is open and the end is closed. This apparatus is used to determine the speed and wavelength of the sound waves. The tube which is present in the apparatus is filled with water and thus the water surface acts as a closed end. A tuning fork which is present on the open end of the tube and is then vibrated which then produces standing waves in the air column. Therefore, the resonance column is both an open and closed system.

2. Why is water used in resonance tubes?

The water fills the space that is not filled by the air. It gives a way to control the exact length of the air column, so when the natural frequency of tuning fork is equal to the frequency of the waves in the air column, the loud sound made in the air column can be heard for maximum amplification, which therefore, means a resonance point have been found at one of the key points for measuring the sound wavelength.

In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter 5 cm is used. The air column in the pipe resonates with a tuning fork of frequency 500 Hz , when the minimum length of the air column is 15.5 cm . Find the speed of sound in air at room temperature.

The correct option is c 340 m/s given, diameter of pipe ( d ) = 5 cm or 0.05 m minimum length of air column ( l m i n ) = 15.5 cm or 0.155 m frequency of tuning fork ( f ) = 500 hz let ′ e ′ be the end correction which is equal to 0.3 d . we know that, fundamental frequency of closed pipe of length l is given by f = v 4 ( l + e ) = v 4 ( l + 0.3 d ) substituting the given data, 500 = v 4 [ ( 0.155 ) + ( 0.3 × 0.05 ) ] ⇒ v = 340 m/s.