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Frequency, Wave Lenght And Wave Velocity

2121 words - 9 pages

Abstract:
The purpose of this experiment was to verify the relationship between frequencies, wave length and wave velocity of a transverse wave on a string, as well as the relationship between the spring tension and the number of standing waves formed. Two different strings used in this experiment are white and black in colour; the µ1 value calculated for the white string is 2.73 x 10-3 ±0.00055kg/m with an uncertainty of ±8.2932 x 10-5 kg/m while the µ2 value calculated for the black string is 1.38 x 10-3 kg/m with an uncertainty of ±8.6492 x 10-5 kg/m. However, the actual linear mass density µ0 of the white spring calculated is 2.87x10-3kg/m; compared to the experimental ...view middle of the document...

Also, the greater the tension on a string the greater the pulling force from one particle to the other; therefore ability of the particle on a string to pull the particle next to it is directly proportional to the tension on the string. The speed of a wave is inversely proportional to its linear density, µ, because the mass of the end particle of the string will affect how fast it will respond to the pull from another particle. The maximum amplitude of a cord can only be achieved if the vibration of the frequency f, length of the cord L, and the speed of the wave on the cord v, is related such that a resonance and a stationary/standing wave are set up. Therefore, the natural frequencies fn, of the oscillation that produced the wave can be determined using the equation fn = {n/2L (√F/µ)} where n is the number of loops (segments between nodes).
Procedure:
The experiment was performed as written in the lab manual “refer to manual”.
Data and Analysis:
Fig 1: showing the graph of experimental frequencies vs. the natural frequencies of vibration of the white string.

The above graph represents the measured frequency vs. the natural frequency. From the graph, we can see that the slope is 19.137 ±0.00055 and the regression on the graph is 0.973, therefore demonstrating a straight line. The µ value for this graph was calculated to be 2.73 x 10-3 ±8.2932 x 10-5kg/m

The above graph represents the measured frequency vs. the natural frequency. From the graph, we can see that the slope is 26.954 ±0.00055 and the regression on the graph is 0.9756, therefore demonstrating a straight line. The µ value for this graph was calculated to be 1.38 x 10-3 ±8.6492 x 10-5kg/m.
Discussion and Conclusion:
In this experiment, the actual linear mass density µ0, calculated is almost the same as the experimental linear mass density µ1. The value of µ0 is 2.87x10-3 ±0.00055kg/m while that of µ1 is 2.73 x 10-3 ±8.2932 x 10-5kg/m and we can see both from these two values that they are directly proportional to each other. The higher the hanged weight the nearer the values of µ0 to µ1 and the higher the tension in the spring thereby producing a higher amplitude. From the graphs, we can see that the linear density increases with increase in tension (increase in mass increases tension in string). Certain errors experienced in this experiment includes error due to the movement of the string along its support as a result of the vibration of the Mechanical Wave Driver, unclear position of the nodes and amplitude of maximum vibration, and error in weight, measurements and how horizontal the tread is. During the experiment, the vibration of the Mechanical Wave Driver causes the string to move along its support and the support to move along the table due to its light weight, therefore producing a non-constant frequency of vibration in the results. This can be corrected by using a more stable or high weighted support to prevent it from move and a...

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