Speed Of Sound In Air At Room Temperature Using A Resonance Tube By Two Resonance Positions

Speed of sound is the rate at which sound waves travel in a medium. Sound waves are often termed mechanical waves because they require a medium to travel. In this experiment, we will learn to calculate the speed of sound in air with the help of the concept of resonance. Resonance is the sound that is produced by an object when it vibrates at the same rate as the sound waves from another object. Using the concept we will calculate the speed of sound at two resonance positions. We use two resonance positions in this experiment to apply end correction. But the experiment can also be conducted by finding the first resonance position only. 

Key Terms: Speed of Sound, Sound Waves, Mechanical waves, Resonance, Antinode, Amplitude, Velocity

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Materials Required

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We have to set up the experiment using a beaker, water, a tuning fork of a known frequency of 480 Hz or 512 Hz, a thermometer, a rubber pad, a set square, spirit level, and resonance tube apparatus.

The resonance tube apparatus is made up of a 1 meter long, 5cm diameter glass tube that stands vertically on a wooden stand. The bottom end of the tube is attached to a reservoir via a rubber tube. The rubber tube has a pinch cock to maintain the desired water level in the tube. Alongside the tube, a meter-long scale is fixed to take readings.

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Principle

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For resonance to occur, a node must be formed at the closed end and an antinode must be formed at the open end. Just like we can see in the second figure a node at the bottom tube. When a vibrating fork is held over the top of the tube a sound wave pattern is formed in the tube. This reflection of wave brings changes into loudness and amplitude of the sound. 

In Figures 3rd and 4th, we will perform the same experiment but with water-filled at different levels. Let the first loud sound be heard at length l1 of the air column. That is when the natural frequency of the air column of length l1 becomes equal to the natural frequency of the tuning fork so that the air column vibrates with the maximum amplitude. In fact, the length of the air column vibrating is slightly longer than the length of the air column in tube AB. Thus

λ / 4 = l1 + e …………..eq (1)

 Where e = 06r (r = radius of the glass tube)

λ = wavelength of sound waves produced by tuning fork

Now in figure 4 we further lower the level of water and define l2. This length l2 would approximately be equal to three-quarters of the wavelength.

3λ / 4 = l2 + e …………..eq (2)

Subtracting equation(1) from equation (2), we get

λ = 2 ( l2 – l1 )

Thus, the velocity of sound in air at room temperature (v = νλ)

Hence,

ðÂÂÂÂÂÂ¥ = 2v (l2  _ l1 )

This formula will be used for calculating observation results and for deriving the speed of sound.

Also Read: Loudness of Sound

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Procedure

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• Setup the whole apparatus and align it properly so that there is no error due to incorrect angles.
• Take the reading for the room temperature using the thermometer.
• Fix the reservoir to the highest point of the vertical rod with the help of a clamp.
• Fill the tube with water up till the open end.
• Close the pinch and lower down the position of the reservoir on the vertical rod.
• Take the tunning fork and use the rubber pad to strike the tuning fork to create the vibration. Keep the tunning fork 1 cm above the open end of the tube, keep both the prongs of the fork parallel to the ground, try to listen to the sound produced in the tube.
• Loosen the pinch cock to let the water level fall slowly, keep bringing the tuning fork near the open end of the resonance tube, notice the increasing loudness of the sound.
• Repeat steps 6 and 7 till you reach the point where the intensity of the sound is maximum.
• This will notify you about the first resonance position.
• Next find out the first resonance position by gradually raising the level of water in the resonance tube, and holding the vibrating tuning fork continuously on top of its open end. Fix the tube at the position where the sound of maximum intensity is heard

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Determining the second resonance point

• Lower the position of the water level further in the resonance tube by sliding down the position of the reservoir on the vertical stand and opening the pinch cock till the length of air column in the tube increases about three times the length l1.
•  Find out the second resonance position and determine the length of air column l2 in the tube with the same tuning fork having frequency ν1 and confirm the length l2 by taking four readings, two when the level of water is falling and the other two when the level of water is rising in the tube.
• Calculate the velocity of sound using the formula.

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Observation

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All the readings from the experiment shall be noted in a table to make calculations easy. The following figure explains the sample table format.

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Calculation

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1.  For the first tuning fork

 V1 = 2v1 ( l2 – l1 )

2. For the second tunning fork 

  V2 = 2v2 ( l2 – l1 )

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Result

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Using the calculations and formulas, derive a mean velocity of sound formula.

(V1 + V2 ) / 2 = mean velocity of sound at room temperature.

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Precaution

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• The resonance should be vertically kept at 900 .
• Avoid noisy places for the experiment, maintain a quiet atmosphere so that the resonance position may be identified properly.
• Choose the resonance fork with different frequencies such that the resonating point could be observed in the tube. Taking large differences in the tubes will hinder the observations and will make it difficult to find the resonating point.
• The vibrating tuning fork must be kept about 1 cm above the top of the resonance tube. In any case, it should not touch the walls of the resonance tube.
• The prongs of the vibrating tuning fork must be kept parallel to the ground and kept one over the other so that the vibrations reaching the air inside the tube are vertical.
• Room temperature during the performance of the experiment should be measured two to three times and a mean value should be taken.

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Things to remember

• Resonance tube must be of uniform area of cross-section
• The velocity of sound depends on the medium of propagation.
• Sound waves travel in standing wave pattern inside the resonance tube.
• The speed of sound waves also depends upon the temperature of the air.
• The vibrating fork should be aligned parallel to the resonance tube 1 cm above the top in order to get accurate results.
• There must be no wind blowing in the room.
• The air inside the tube may not be completely dry and the presence of water vapors in the air column may exhibit a higher value of the velocity of sound

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