April 3, 2019
Lab Group: Jared, Jacob, Tyler, Zach
Lab Group: Jared, Jacob, Tyler, Zach
Procedure and Calculations
In this lab we were tasked with determining the linear mass density of a string using our knowledge of mechanical waves. The speed of a wave through a string is the square root of the string's tension over its linear mass density. Solving for linear mass density reveals that the string's linear mass density will be equal to the string's tension over the speed of the wave squared. To measure the speed of waves through the string, we observed standing waves. Standing waves are created when waves travel down the string and reflect back up, adding constructively and destructively to give the appearance of a stationary wave on the string. These standing waves occur when the string is oscillated at certain frequencies.
The group fastened one end of the string to a wave generator to control the frequency of the wave. To measure the tension on the wave as it was being oscillated, we looped the other end of the string through a pulley so that the end hung vertically. On the end of the string we placed a 200g mass which exerted a 19.6N tension force on the string as it was being oscillated.
We used the the frequency and the wavelength of the standing wave created using the wave generator to determine the speed that wave traveled through the string. The speed of a wave is the product of its wavelength and its frequency. We adjusted the oscillation frequency and noted that at 31 Hz a standing wave with three antinodes appeared on the string. The string was 1.16 m long from the wave generator to the pulley, so the wavelength was two thirds of the length of the string, 0.773m. Using these values we calculated the speed of the wave to be 24.0 m/s. Using this value as well as the 19.6N tension force yields a linear mass density of 0.0342 kg/m.
Uncertainty Analysis
There are multiple factors of uncertainty that could have influenced our measurements. We only used one frequency and wavelength to determine the speed of the wave traveling through the string, while other harmonic frequencies with different numbers of nodes and antinodes and therefore different wavelengths should yield the same speed. Averaging multiple standing wave frequencies would have yielded more accurate results. Additionally, running multiple trials with different masses would provide a wider dataset and further improve accuracy. However, the string we tested did stretch slightly when a force of tension was applied. As a result, it is possible that actual linear mass density of the string would not remain constant when different forces of tension are applied. One possible way to compensate for this would b to measure the total length of the string with each new force of tension.
Widget is not loading comments...