Physics 1408 Lab Report 10 PDF

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Physics 1408 Lab Section B1

Standing Waves in a Vibrating Wire Eric Mora Partner: Joelle Fornasier Date Performed: October 29, 2018 TA: Katrina Vermillion

Abstract The objective of this experiment was to try and determine the relationship between the length of a stretched wire and the frequencies it resonates at as well as the relationship between the tension of the strings and their velocities. The relationship between the frequencies of vibration and tension and the mass density of the wire was also tested. The mass density for the three tables was calculated to be: 0.46 g/m for 2a, . 559 g/m for 2b, and .449 g/m for 2c. The percent difference of these values and the accepted values for each table was calculated to be: 2a at 59.95%, 2b at 37.32%, and 2c at 40.11%. Discussion For this lab, wire strings of three different lengths (0.014 in, 0.017 in, and 0.020 in) were taken and stretched out on an apparatus called the sonometer. A hanging mass was hunger off the end of the lever of the apparatus so that it would put weight (1.00 + 0.05 kg) on the wire string and create tension. The lever had five notches in-grooved in it and these notches caused the wire to be pulled at different tensions. With the help of a tool known as the detector coil, we were able to record the signal frequency of each string. Multiplying these factors by two gives the values for wire frequency. The wavelengths of each harmonic were calculated using the equation; wavelengths= (2 * L)/n. For the remainder of the experiment however, only the first harmonic was tested for the remaining trials (120 m). Using the equation of (wire frequency) * (wavelength of the first harmonic) we were able to calculate the velocity of the vibrating string on each knot. This information was found three separate times with each different length string.

For each of the three trial, the mass density of wire from the graph was required. In order to find this, a graph was needed for each length of string and the y-intercept needed to be determined. The X values of the graph were calculated from ln (Tension) (N), while the Y values were calculated from ln (Velocity) (m/s). Nothing else was done for these equations besides plugging in the already found values of velocity and tension. The mass density of the wire was found from the equation: mo=e (-2 (y-intercept)) Using this equation, the mass densities were determined to be; 0.46 g/m for 2a, .559 g/m for 2b, and .449 g/m for 2c. The accepted values for these strings were; 0.78 g/m for string 0.014 in, 1.12 g/m for 0.017 in, and 1.50 g/m for 0.02 in. These two values were compared for each string and the percent differences were found to be 59.95 % for trial 2a, 37.32 % for trial 2b, and for the last trial, 2c, it was 40.11%. Observing the graph shows that there is a correlation between the ln (tension) and the ln (Velocity). As tension increased, the velocity seemed to increase as well. There were a few sources of error that could have had an affect on the data. The main source of error was that it was difficult to visually determine, with no actual way to check our assumptions, where the different harmonics were. If these first values were wrong then the signal frequency could be off which would throw the rest of the calculations off as well....