Speed of sound using resonance column

Introduction:

We can find the velocity of the sound in any medium if we know the frequency and the wavelength of the sound wave. The relationship between these quantities can be given as ,

                                                                v =ט ג ,

where v = velocity of sound propagation, ט = frequency and ג = wavelength of the sound wave. In this article we will study to find the velocity of sound in air by the use of tuning forks. The frequencies of these tuning forks will be known to us. We will get the resonance condition in a resonance tube which is a hollow cylindrical tube. It is partially filled with water. Tuning fork is used to produce vibration. These  vibrations produce standing waves in the resonance tube. The resonance condition is achieved by adjustment of water levels in the resonance tube. We will use the resonance phenomenon in an air column to determine the wavelength of the sound.

Resonance in Air Column 

The resonance in the air column is a condition in which we get maximum loudness of the sound in the air column. This resonance condition is obtained by the superposition of incident sound waves and reflected sound waves in the air column.

Determination of Velocity of Sound in Air Column 

Our first aim is to obtain the condition of resonance in the resonance tube. We will use a tuning fork to produce the sound wave. We get compression and rarefaction in the air region from the vibration obtained from the tines of a tuning fork. If we send these disturbances to an air filled tube then it is reflected back to the upper end of the tube from a fixed boundary. Due to this, there is interference between the two waves. One wave is an incident wave sent by us into the tube and the other wave received after reflection from the fixed boundary of the tube. 

 If we choose the distance from the open end of the tube to the closed end appropriately, then a standing longitudinal wave is formed in the tube which creates a resonance condition. The resonance in sound waves is indicated by an increase in the loudness of the sound. In this resonance condition, on the water surface a node of standing wave is formed as the air is not free to move longitudinally and at the open end we have an antinode.

 As we know that one full wavelength of a wave is the distance between two nodes and the antinode is halfway between the nodes. So, the distance from an antinode to a node corresponds to ג4 ,  3ג4 ,  5ג4  ,etc of a wavelength. 

The position of the anti-node at the open end of the tube cannot be precisely located so the distance from the open end to the first node is not considered. We measure the distance from one node to the next adjacent node at the resonance condition. We will take a long cylindrical plastic tube attached to a water reservoir.

 We can change the length of the water column by raising or lowering the water level while the tuning fork is held on the top open end of the tube. 

Equipment required

(i) Apparatus for Resonance Tube

(ii) Three different tuning forks of the known frequency with error ± 0.5 %

(iii) Hammer/rubber mallet for tuning forks

(iv)  Plastic beaker and bulbs for removing water

(v) Thermometer with error ± 2° C

Procedure

1. We will fill the tube with water. 
2. We will strike one of the tuning forks with the rubber mallet/hammer and hold it above the water column such that it does not touch the tube.
3. We will adjust the level of the water by using a water reservoir to get the sound with maximum intensity i.e. the condition of resonance.
4. We will mark this point on the outside of the tube.
5. We will lower the water further to find the next resonant length. 
6. We will continue the above mentioned steps as far as the length of the tube permits. 
7. We will obtain the lengths λ/4, 3λ/4, etc in metres from our measurements and check the progression of the column lengths as 1, 3, 5, 7. We will calculate the wavelength and velocity of sound.
8. We will repeat the procedure for the other tuning forks. 
9. To get the velocity of the sound in miles per hour we will multiply the velocity in m/sec by the factor of 2.24. 
10. We need to record the room temperature for our reference as the velocity of sound increases with an increase in the air temperature.

Conclusion

In this article, we learned to get the velocity of sound waves by using resonance phenomena in air columns. We sent sound waves produced by a tuning fork down to a tube filled with a liquid. The waves reflected back up the tube from a water surface interfere with the waves travelling downward to make a standing wave. We obtained resonance conditions by the proper adjustment of the water level. We calculated the speed of the sound waves by knowing the frequency of the tuning fork of known frequency and the position of the water level at two different resonant lengths.