Experimental physics
The speed of sound
Introduction
In this investigation you will be using different frequency sound signals to find the fundamental frequency of an air column (tube). You will then be making use of this to calculate the speed of sound in air. This investigation is designed to give you an understanding of:
• Resonance
• Standing waves in air columns
• End effects
Theory
For an air column closed at one end, resonance occurs under the following condition:
where L is the length of the air column and n is the harmonic. In the figure on the right you can see the first harmonic (fundamental), third harmonic and fifth harmonic.
Equation for the speed of a wave
Equipment
Assemble this equipment before you start the exercise:
• A cardboard/PVC tube around 4 cm in diameter and at least 20 cm long (the carboard tube found at the centre of a roll of paper towel or wrapping paper is perfect).
• A bucket/tall container (this needs to fit the length of the tube)
• A ruler
• A tablet or smartphone with a tone generator app. (Free or low-cost apps are available.)
• A set of earphones
Questions
1. You are hearing the resonance caused by the fundamental mode of the vibration of this tube. Sketch a diagram showing the displacement of the air particles from their equilibrium positions along your tube when it is resonating at this mode. What proportion of a wavelength is inside the tube at this fundamental mode?
If you find it difficult to type your working draw diagrams for your document, then you can do your work with pen/pencil and paper and insert an image of it into your report.
2. In reality, the antinode of the wave does not occur at the opening of the tube, but just outside the tube – this phenomenon is often referred to as an “end effect”, often estimated to be 0.6 times the radius of the tube.
Describe how could you use your results to estimate the size of the end effects. Use this method to estimate the end effects for your tube. How does your result compare to the estimate of 0.6 times the radius of your tube? You should refer to your uncertainties when you answer this question.
3. For the highest frequency you used estimate what length of tubing you would need sticking out a bucket of water (L in figure 1) to hear the next two harmonics. Sketch diagrams showing the displacement of the air particles from their equilibrium positions along the pipe for these two harmonics.
4. How does your result for the speed of sound in air compare to the accepted result (you should look up what this is)? Explain any discrepancies between your result and the expected result. Make sure that you reference your uncertainties in answering this question.