Standing Waves

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Investigating The Variation of Wavelenght on Standing Waves:
The Relationship between the Tension and the Wavelenght of a Standing Wave

Research Question:
How is the wavelenght of a standing wave dependent on the tension applied on the string?

Hypothesis:
If the tension on the string increases, the wavelenght of the standing wave will increase.

Aim:
To investigate the relationship between the Tension and the Wavelenght of a Standing Wave.

Introduction: As a musician myself, I have always been extremely interested in how sound is produced in an instrument due to the tension caused by different lenghts of strings. Since the age of five, I have been playing the piano. Each time, I pressed a key on the piano, the sound would be completely
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Moreover, as the velocity of the string increases, the wavelenght increases. As a result, it can be stated that tension and wavelenght has a direct relationship between each other.

Method:

The experiment will be conducted by applying tension the string, creating a standing wave, and measuring the wavelenght accordingly. By this method, I will be examining the dependence of the wavelenght of a standing wave, to the tension applied on the string.

1) I will tie one end of the string on the stand.
2) The string’s other end will go through the pulley and will be attached to different masses (0.07kg, 0.09kg, 0.10kg, 0.11kg, 0.15kg) dependent on the length.
3) These masses will cause tension on the string. (Gravity will be accepted as 9.81)
4) The mass chosen will help me conduct a standing wave.
5) I will use a magnet and a 50 Hz frequency to create a standing wave with four antinodes. (The 50Hz frequency will be provided by the AC city current.)
6) I will measure the length of the string once the standing wave has been
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Random errors are something that you can reduce by repeating the measurements, so the errors associated with my measurement methods are random errors, such as the length measurements.

An example of systematic errors could be calibration errors of equipment. These errors will always be there even if you repeat your measurement many times. In this case, the uncertainties in the masses that I used could be systematic, because they are always there. It says 70g on it but it is actually 70.7g etc. So that is a king of calibration error.

However, although the frequency I calculated resulted as 41.5Hz, this value does proves the theoretical formula. It is not exactly the same as 50 Hz, but there are uncertainties with 41.5 Hz. Therefore, my result is very close to the actual value.

From these results, we can conclude that the relation between tension and wavelength is direct. Consequently, using the data, I proved that my hypothesis was correct and they are related as in the formulas presented.

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