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# The aim of this experiment is to investigate the relationship between the length of a closed tube and the frequency of the lowest fundamental note.

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Introduction

Length and frequency of a fundamental note Aim: The aim of this experiment is to investigate the relationship between the length of a closed tube and the frequency of the lowest fundamental note. Plan: Clamp and clamp stand Speaker Ruler Hollow tube (diameter 0.025m) Signal generator Measuring cylinder Water The experiment will be setup as shown in fig 1. Method: The Hollow tube is suspended by the clamp stand in the measuring cylinder which is filled with water. This effectively seals it off creating a closed ended tube that can have the length adjusted by moving the tube up and down in the water. The length of the tube is then measured from the top to the waterline. The speaker is connected to the signal generator and is suspended above the tube. The signal generator will go through frequencies from 200Hz to 560Hz at 40Hz intervals (this was previously decided, the evenly spaced samples will make finding a relationship easier). At every frequency the tube will be moved up or down until it is in the position that creates the lowest loud noise possible (without changing anything else). ...read more.

Middle

1/f is the time of one wavelength. ? is the wavelength. This was calculated by v*1/f where v is the speed of sound. This was accurately adjusted to the air temperature (because sounds speed changes in different temperatures) with v= 331.5+(0.6*T) T is the room temperature in �C which in this case was 21.5�C which makes the speed of sound 344.4. L=(?/4)-d is the length calculated with a formula designed for use with tubes where d is the diameter of the tube, 0.025m in this case. L=(?/4) is the length calculated with the standard formula for standing waves caused by being bounced off a surface. L is the measured tube length. Conclusion: As expected the measured results fit well with the existing rules of standing waves. from s-cool.co.uk This diagram shows a standing wave. The x points are nodes where the waves add up to zero and the y points are antinodes where the waves combine to give a large oscillation. The fundamental note is reached in a tube when there is just one node as this diagram shows: This creates the lowest possible resonance. ...read more.

Conclusion

To improve this the measurement marks could be marked on the tube to reduce the risk of human error and a flat piston inside the tube could be used instead of water because its more accurate than the surface of water. Also there was a reliance on the human ear to detect where the fundamental note was. This is a very inaccurate way of detecting it because it isn't that sensitive compared to electronic equipment. It would be better to instead use a microphone connected to an oscilloscope to be able to accurately visually check where the fundamental note is. The other inaccuracy is in the control of the environment around the experiment. It would be better to do the investigation in a controlled area where the temperature is guaranteed to remain constant and thus the speed of sound. Also the use of water as a reflective surface may cause unknown affects as it is able to move. There is a chance that some of the sound waves can be absorbed by it and the vibrations caused by the oscillations in the tube when standing waves occur could cause ripples on the water which would in turn affect how the sound wave reflects off the water. It would be better to instead use a solid surface. ...read more.

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