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An investigation into the factors affecting the frequency of a standing wave

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Introduction

An investigation into the factors affecting the frequency of a standing wave

Introduction

There are several ways in which you can control the pitch (frequency) of a note produced by a string.

A string with 2 fixed ends (called nodes) can produce different standing waves. The lowest frequency standing wave that can be produced has a wavelength λ where

                        λ = 2ℓ   (ℓ = length of string)

This is related to the frequency ƒ of oscillation by the wave equation

                        V = ƒλ

Where V is the speed of transverse waves traveling along the string. You can therefore deduct that

                        ƒ = v/λ = v/2ℓ

ƒ therefore should be inversely proportional to the length of the string, i.e. the shorter the string, the higher the note.

The frequency will also depend on the tension and the mass per unit length of the string, as they affect the speed of transverse waves traveling along the string. The greater the tension, the greater the speed, and the heavier the string, the lower the speed.

This becomes important in this investigation because if the experiment is to be fair, then the two other factors affecting the frequency must be kept constant for the results to be accurate.

I have decided to investigate the effect that altering the length of string along which the wave travels.

...read more.

Middle

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Using the signal generator which will be connected to either end of the length of wire, different frequencies can be used to create standing waves down different lengths of wire.

I will use different lengths of wire to see what frequency is needed to produce a clean standing wave, which can be seen by the magnet’s field interacting with the electric field causing a movement in the wire at a 90° angle. Therefore it will be obvious at which frequency the wire oscillates also because a note, like a hum, will be produced.

The lengths of wire I will use can be changed from 100 cm to about 40 in 10 cm intervals by measuring with a metre stick, accurate to a mm, to the place on the wire where the moveable node needs to be.

Although you can read off the signal generator what the frequency needed to make the wave is, it is very inaccurate as it only reads off to the nearest Hz. Therefore, I decided to link the signal generator to the cathode ray oscilloscope and use the graph created on the screen to read off the time period, as this can be used to find the frequency of the wave.

...read more.

Conclusion

When turning the dial on the signal generator, it was very hard to turn it precisely enough to create the right frequency which would have made the wire resonate, and sometimes it could have been seen beating which signified that the frequency was not correct. This could have been avoided by having a more sensitive signal generator.

The CRO display was very hard to read off of, and probably increased the inaccuracy. If it had had smaller gridlines, or an indication of where the troughs of the wave were, then the results would have been more accurate.

Altogether, the inaccuracy which is plotted on my graph seems about right, and the experiment could have been improved by using more sensitive equipment, possibly a computer, to show that frequency is inversely proportional to wavelength, i.e.:

                                 ƒ = v / λ

...read more.

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Here's what a teacher thought of this essay

4 star(s)

This is a well written report that lacks structure.
1. There are several subheadings missing.
2. The table of results needs to be included.
3. The conclusion needs to quote data from the investigation.
4. The evaluation needs to suggest further opportunities.
****

Marked by teacher Luke Smithen 13/08/2013

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