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# Making Sense of Data.

Extracts from this document...

Introduction

Mike Hodges

Making Sense of Data

A loudspeaker is held over a glass tube, one end of which is submerged in water.  The frequency from the signal generator is set, and the tube is moved until it resounds at the fundamental frequency, causing a raise in volume.

This raise in volume is caused by the manner in which the sound waves travel through the tube.  The wave travels down the pipe, is reflected off of the water, and leaves the tube.  There is a node at the closed end, as the air in contact with the water is permanently at rest, and an anti-node at the end of the pipe, where the air is free to vibrate.

Middle

These vibrations extend a little out of the edge of the tube.  The distance extended, or end correction (c), is directly proportional to the radius of the pipe:

You can also find the end correction by constructing the graph with the reciprocal of the frequency against the length of the pipe.  The difference between zero and the point at which the trend line crosses the x-axis will give you the end correction of the pipe.

This is the equation of the trend line.

= 0.0118 + 0.0001

Therefore, when  = 0:

Hence, the end correction of the tube is 0.0085m.

Using the relationship:

c = 0.6 × 0.012m

c = 0.0072m

The result I obtained from the graph differs slightly to this.

Conclusion

My experiment was successful, but my results vary slightly from those achieved with the different formula.  My judgement of the fundamental frequency will also have a major effect on my results.  Another source of error could be the signal generator.

With the equipment I was given, I could only take measurements to the nearest millimetre, and if I were to redo this experiment, I would try to take results that are more accurate.  In addition, I would use a wider range of frequencies, as this may be the reason for differences with the worked answers.

Despite most of my results being acceptable, I did however obtain one anomalous result.  This result, highlighted in the table, has not been included in any averages, or graphs.

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