in resonance tube experiment if 400 hz

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 c m for a tuning fork of frequency 400 H z is used. The velocity of the sound at room temperature is 336 m s – 1 . The third resonance is observed when the air column has a length of cm

400 = v 4 ( l 1 + e ) . . . ( i ) 400 = 5 v 4 ( l 2 + e ) . . . ( i i ) ⇒ l 1 + e = λ 4 = 21 c m l 2 + e = 5 λ 4 = 105 c m ⇒ e = 1 c m & l 2 = 104 c m.

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 ?

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• To Find the Speed of Sound in Air at Room Temperature Using a Resonance Tube By Two Resonance Positions

Resonance in an Air Column

The physics practicals play a crucial role in helping the students understand the concepts better by doing them practically. It offers them hands-on experience of how the phenomenon takes place. We provide the complete experiment, how to conduct it, the substitution of values, and the further procedure that follows. With the resonance experiment Class 11, you can better understand the resonance concepts. We provide these experiments in PDF downloadable form to conduct them easily and quickly while you are at work . 

What is Resonance?

Before jumping directly into the experiment, let’s recall what Resonance is. 

When a person knocks, strikes, strums, plucks or otherwise disturbs a musical instrument, it is sent into vibrational motion at its inherent frequency. Each object's native frequency corresponds to one of the several standing wave patterns that might cause it to vibrate. The harmonics of a musical instrument are commonly referred to as the instrument's inherent frequencies. If another interconnected item pushes it with one of those frequencies, it can be compelled to vibrate at one of its harmonics (with one of its standing wave patterns). This is known as resonance, which occurs when one thing vibrates at the same natural frequency as another, causing the second object to vibrate.

Resonance Tube

A resonance tube (a hollow cylindrical tube partially filled with water and driven into vibration by a tuning fork) is one of our finest models of resonance in a musical instrument. The tuning fork was the item that induced resonance in the air inside the resonance tube. The tines of the tuning fork vibrate at their natural frequency, causing sound waves to impinge on the resonance tube's aperture. The tuning fork's impinging sound waves cause the air within the resonance tube to vibrate at the same frequency.

In the absence of resonance, however, the sound of these vibrations is inaudible. Only when the first thing vibrates at the inherent frequency of the second object does resonance occur. If the tuning fork vibrates at a frequency that is not the same as one of the natural frequencies of the air column within the resonance tube, resonance will not occur, and the two items will not make a loud sound together. However, by raising and lowering a reservoir of water and therefore decreasing or increasing the length of the air column, the position of the water level may be changed so that the air column vibrates with the same frequency of the tuning fork causing the resonance to occur.

Experiment to Find the Speed of Sound in Air

The aim is to find the speed of sound in air at room temperature using a resonance tube by two resonance positions. 

Apparatus Required for Resonance Experiment Physics:

Resonance tube

Two-timing forks having frequencies that are known (for example, 512Hz and 480Hz)

Thermometer

Set squares

Water contained in a beaker

Consider the length of two air columns for first and second resonance as l 1 and l 2 . Let the frequency of the tuning fork be f. 

Then, the formula is

\[\lambda = 2\left ( I_{2}- I^{_{1}} \right )\]

The speed of air is calculated using the formula:

\[ v= f\lambda\]

On substituting the value in the formulae, we get, 

\[v = 2f\left ( I_{2}- I^{_{1}} \right )\]

The Procedure of the Resonance Tube Experiment:

Make the base horizontal by the levelling screws. Following this, keep the resonance tubes vertical. 

Next, in the uppermost position, fix the reservoir R. 

Make the pinchcock lose. Fill water from the beaker in the reservoir and metallic tube. 

Fix the reservoir in the lowest position, by lowering the reservoir and tightening the pinchcock. 

Next, use a tuning fork of higher frequency to experiment. 

Vibrate this tuning fork with the help of a rubber pad. Just over the end of the metallic tube, hold the vibrating tongs in a vertical plane. 

Next, loosen the pinchcock a bit to allow the water to fall into the metallic tube. When you hear the sound from the metallic tube, lose the pinchcock a bit. 

Repeat the above step till you hear the sound with maximum loudness from the metallic tube.

By using the set square, against the meter scale, measure the position of the water level. 

Decrease the water level by 1 cm. And then tighten the pinchcock. 

Again, repeat the above step till maximum loudness is heard. 

After this, repeat the steps with a tuning fork of lower frequency. 

Record your observations and put them in the resonance tube formula as given below:

Observations:

The temperature of the air column:

In the beginning:

At the end:

Calculate the mean temperature using the formula:

\[t = \frac{t_{1}+t_{2}}{2}\]

f 1 = frequency of the first tuning fork

f 2 = frequency of the second tuning fork

Calculations:

Observations from the first tuning fork,

\[v_{1} = 2f_{1}(I_{2}'I_{1}'))\]

Observations from the second tuning fork,

\[v_{2} = 2f_{2}(I_{2}”I_{1}”))\]

Calculate the mean velocity using the formula:

\[v = \frac{v_{1}+v_{2}}{2}\]

The speed of air at room temperature is ____ m/s.

Precautions :

Keep the resonance tube vertical.

Ensure that the pinchcock is tight. 

Vibrate the tuning fork lightly using the rubber pad. 

While vibrating the prongs, ensure that they are vertical at the mouth of the metallic tube. 

Carefully read the water level rise and fall. 

Use a set square to record the readings. 

Sources of Error:

Loose pinchcock. 

Resonance tubes might not be uptight. 

The air column contains humidity which can lead to an increase in velocity. 

1. What is the working principle of the resonance tube?

Answer: The idea of the resonance tube is based on the resonance of an air column with a tuning fork. Transverse stationary waves are formed in the air column. The wave's node is at the water's surface, while the wave's antinode is at the tube's open end.

2. What types of waves are produced in the air column?

Answer: The air column produces longitudinal stationary waves. The standing wave is another name for a stationary wave. Standing waves are waves with the same amplitude and frequency travelling in the opposite direction. Longitudinal waves can also generate standing waves.

3. Do you find the velocity of sound in the air column or in the water column?

Answer: The sound velocity is determined in the air column, which is above the water column.

4. What are the possible errors in the result?

Answer: The following are two probable inaccuracies in the result: 

Because the confined air in the air column is denser than the outside air, the air velocity may be reduced.

Humidity in the air above the confined water column may enhance sound velocity.

5. Will the result be affected if we take other liquids than water?

Answer: It will not be altered in any way.

FAQs on To Find the Speed of Sound in Air at Room Temperature Using a Resonance Tube By Two Resonance Positions

1. On what principle does the resonance tube work?

The idea of the resonance tube is based on the resonance of an air column with a tuning fork. Transverse stationary waves are formed in the air column. The wave's node is at the water's surface, while the wave's antinode is at the tube's open end.

2. Define the resonance of the air column?

The phenomenon of resonance is defined as the frequency of the air column is equal to the frequency of the tuning fork. A variable piston adjusts the length of a resonance air column, which is a glass tube. The two subsequent resonances seen at room temperature are at 20 cm and 85 cm in column length. Calculate the sound velocity in the air at room temperature if the length's frequency is 256 Hz.

3. During vibration, what are the types of waves being produced in the air column?

Longitudinal stationary waves are generated in the air column while measuring the speed of sound at room temperature.

4. What is end correction?

End correction is defined as the reflection of a sound wave from the end of the tube (slightly above it).

5. How do you find the velocity of sound in air?

It is found using the air column lying above the water surface.

6. What are some of the errors that can occur while calculating the result?

There are two majorly possible errors:

If the air enclosed inside is denser than the air outside, it can reduce the velocity of sound. 

The velocity of sound can be increased if the air above the column has increased humidity. 

( Note. The ideal observations are as samples.)