Step-by-Step Guide: Measuring Speed of Sound Using Two Resonance Positions
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
Aim:
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)
Rubber pad
Thermometer
Set squares
Water contained in a beaker
Plumb line
Theory:
Consider the length of two air columns for first and second resonance as l1 and l2. 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:
\[t = \frac{t_{1}+t_{2}}{2}\]
f1= frequency of the first tuning fork
f2= 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:
\[v = \frac{v_{1}+v_{2}}{2}\]
Result:
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.
Viva Voce
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 Speed of Sound in Air at Room Temperature: Resonance Tube Method
1. What is the working principle behind finding the speed of sound using a resonance tube?
The experiment works on the principle of resonance of an air column. When a vibrating tuning fork is held over the open end of the tube, it sends sound waves down the air column. These waves reflect off the water surface. At specific lengths of the air column, the frequency of the vibrating air column matches the tuning fork's frequency, causing resonance and producing a loud sound. This setup forms longitudinal stationary waves with a node at the water surface and an antinode near the open end.
2. What is the formula used to calculate the speed of sound using the two-resonance position method?
The speed of sound (v) is calculated using the formula v = 2f(l₂ - l₁). Here, 'f' is the frequency of the tuning fork, 'l₁' is the length of the air column for the first resonance, and 'l₂' is the length of the air column for the second resonance. This formula is derived from the fact that the distance between two successive resonance points is equal to half the wavelength of the sound wave (λ/2).
3. Why is using two resonance positions preferred over using a single position in this experiment?
The two-resonance position method is preferred because it effectively eliminates the end correction from the calculation. End correction is a small error caused by the antinode forming slightly above the open end of the tube. By taking the difference between the two resonating lengths (l₂ - l₁), the end correction factor cancels out, leading to a more accurate and reliable measurement of the speed of sound.
4. What is 'end correction' in a resonance tube and why does it occur?
End correction is the small distance that must be added to the resonating length of the air column to get the effective length. It occurs because the air particles just outside the open end of the tube are not perfectly free to vibrate and are part of the standing wave pattern. As a result, the antinode is not formed exactly at the open end but slightly above it. This distance is the end correction, typically estimated as e ≈ 0.6r, where 'r' is the radius of the tube.
5. Is a resonance tube considered an open pipe or a closed pipe? Explain why.
A resonance tube is considered a closed organ pipe. This is because it is open at one end (where the tuning fork is placed) and closed at the other end by the water surface. This configuration creates a specific boundary condition for wave reflection: a node (a point of zero displacement) is always formed at the closed end (the water surface), while an antinode (a point of maximum displacement) is formed near the open end.
6. How does the room temperature affect the speed of sound measured in this experiment?
The speed of sound in air is directly affected by temperature. Specifically, the speed of sound is proportional to the square root of the absolute temperature (v ∝ √T). Therefore, if the room temperature increases, the measured speed of sound will also increase. It is crucial to measure and note the room temperature during the experiment to either calculate the speed at 0°C or to compare the result with the standard value at that specific temperature.
7. What are some common sources of error in the resonance tube experiment?
The main sources of error in this experiment include:
- Judgement of Resonance: It can be difficult for the observer to accurately identify the exact point of maximum sound intensity, leading to errors in measuring l₁ and l₂.
- Tuning Fork Position: The tuning fork might not be held perfectly horizontally or at the centre of the tube's mouth, affecting the resonance.
- Non-Uniform Tube: If the diameter of the resonance tube is not uniform throughout its length, it can affect the wave pattern.
- Temperature Fluctuations: Any change in room temperature during the experiment will alter the speed of sound and affect the accuracy of the final result.
8. What would happen if the tuning fork touches the rim of the resonance tube during the experiment?
If the vibrating tuning fork touches the glass tube, its vibrations will be directly transferred to the tube itself. This creates forced vibrations in the glass, which will interfere with the pure resonance of the air column. The sound produced will be a mix of the air column's resonance and the tube's own vibration, making it nearly impossible to accurately locate the point of maximum sound intensity. This will lead to a significant error in measuring the resonating lengths.
