|
 |
 |
 |
 |
 |
 |
 |
 |
 |
| A system was set up and analyzed for the purpose of measuring the value of linear density of a length of string through direct and indirect experimentation. A weight tied to the end of a string was used to create a calculable tension in the string. A variable frequency generator was used to obtain a periodic vibration in the string, while a small wooden block was placed under it to maintain a easily measured fixed length. While varying the frequency, to a maximum of 350Hz, whenever a standing wave pattern appeared, the number of nodes and the frequency was recorded. Using this data, a value for linear density was calculated for each recording, and then averaged, yielding a result of 1.42x10-4 kg/m, a 14.4% deviation from the theoretical value of 1.66x10-4 kg/m. By plotting the values on an x-y graph, the slope was measured and used to obtain a linear density of 7.52x10-3 kg/m, a 54.6% difference from the previously obtained theoretical value. The theoretical result was found simply by measuring the mass of a known length of string, and then dividing the values. In conclusion, three separate values for linear density were found, and all were within an acceptable range of each other. The discrepancies can be accounted for mostly through experimental error (eg tension did no hold string tight enough on wood block, stretching of the string, frequency generator was not calibrated correctly?) |