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Physics Laboratory - "Waves in Strings".

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Introduction

Dmitri Ramzaitsev

30.11.03        11B

Physics Laboratory – “Waves in Strings

Data Collection

The Harmonic Number

2

3

4

5

The Number of Nodes

1

2

3

4

Mass Pulling the String (in Kg)

0.3

0.1

0.030

0.015

This data does not include any uncertainties purposely.  While the experiment was carried out, I noticed that the number of harmonics was not so clear every time.  The mass at the end of the string could be change to ± 0.015 kgand we could not see any difference in the number of nodes.  The additional mass simply displaced the nodes a little, but created none.  Therefore, it is safe to say that there was no specific or accurate mass that we measured to create each harmonic.  And because the masses that

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Middle

0.100

0.030

0.015

Gravitational Force of Mass in Newtons

2.94

0.981

.294

0.147

The Square Root of Force (to 3 s.f.)

1.72

0.990

0.542

0.383

The Inverse of the Square Root of Force (to 3 s.f.)

0.582

1.01

1.84

2.61

2.), 5.)  See attached sheets please.

B.1.) There is a clear relationship between the number of harmonics and the force pulling on the string. As the harmonics increase the mass hanging decreases exponentially.  

    2.) See graph for working out.  Our graph starts from the second harmonic, since we only got results starting from the second one.  It is quite clear, just by looking at the graph that it is exponential and if you continue the line beyond what the graph shows us, you can estimate what force would be needed for the 1st harmonic. It is around 4.9 N.

    3.) The graph “The Relationship Between the Inverse of the Square Root of Force (to 3 s.f.) to the Number of Harmonics” shows, more or less, a straight line.  The means that the graph has a constant slope and therefore there is a direct proportionality between the x-axis and y-axis values.  

    4.)  Nothing happened when we placed our finger at a node.

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Conclusion


        It also seems logical that, when you tune a guitar string and you increase the tension, the frequency increases giving you a higher pitched sound.  Yet if you theoretically keep the frequency constant, you should be increasing the wavelength, which you’re NOT doing in this experiment.  In this lab, as the tension increased, the wavelength decreased, and we lowered the harmonics.  

        Nevertheless, there is clearly some relationship between the tension in the string and the harmonic.  

Evaluation

This lab showed a clear proportion between the tension and the harmonics in a standing wave.  However, there were weaknesses in the procedure.  It was very difficult to decide upon when the standing wave has a certain amount of nodes.  This is because the mass did not have a great affect if it was ±0.015 kg.  This made our data collection weak and made it useless to use uncertainties.  This is because there is a great human error in this experiment.  Perhaps the procedure should help us distinguish a “real” node, so that we can be certain of which force is needed to create it.  


[1]1, 2Source:  http://carini.physics.indiana.edu/P105S98/Standing-waves.html

[2]

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