Experiment #12_ Standing Waves Lab - Kyra Burnside

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Experiment #12 Standing Waves Kyra Burnside Prof. Safaie Engineering Physics 105 12/14/2021

Standing Waves Lab Introduction: The purpose of this lab is to understand the behavior of the waves of a string when the string interacts with different tensions, amplitudes and damping settings. To do this we are using two different simulators. One will show us the harmonics of frequencies and another will allow us to manipulate factors in order to create wavelengths. When we manipulate these factors just right, we will begin to see harmonics. These harmonics will be the focus of our experiment as we try to understand and predict them. The hypothesis is that we will be able to predict harmonics with decent accuracy using the previous data we have already collected and our simulators. This experiment is interesting because the idea of frequency and wavelength is used in many applications such as sound, color and developing technologies. This can help us understand those applied fields, as well as many others. Results: Part 1: Waves on a String With No End Challenge: Determine the speed of the waves at each tension setting (high, medium and low). Explain what measurements you made to calculate the speed. Settings: amplitude: 0.75 cm damping: zero high tension: medium tension: low tension: Does the speed of the wave depend on the frequency or is it the same for all frequencies? Collect data to support your answer: The speed of the wave depends on the frequency. The higher the frequency, the higher the speed of the wave and vice versa. This can be seen in the following screenshots where the first frequency is 1.00 Hz and the second frequency is 3.00 Hz. Both waves have the same amplitude, dampness and tension. The wave in the second screenshot is moving faster because the frequency is higher than the frequency of the first screenshot, where the wave is slower.

---- Part 2: Waves on a string with a fixed end Challenge: Draw and measure the frequencies of the 4 th , 3 rd , 2 nd , and 1 st harmonics. Settings: amplitude: 4 cm tension: high damping: none (4 antinodes) (3 antinodes) (2 antinodes) (1 antinode) f 4 = 0.267 Hz f 3 = 0.201 Hz f 2 = 0.134 Hz f 1 = 0.067 Hz Divide each higher harmonic by the first harmonic: f 4 / f 1 = 0.251 Hz f 3 / f 1 = 0.502 Hz f 2 / f 1 = 0.753 Hz Are the higher harmonics whole-number multiples of the first harmonic (fundamental frequency)? Yes, because 0.0665 (rounded) can be added to a previous harmonic to get the next one. Predict the frequency of the 5 th harmonic: (show calculation) 0.334 Hz, because 0.2675 + 0.0665 equals 0.334 Hz. Set the wave driver to that frequency and draw the result here: ---- Part 3: Waves on a string with a loose end

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Challenge: Draw and measure the frequency of the 1 st harmonic (node near driver end followed by an antinode on loose end) Settings: amplitude: 4 cm tension: high damping: none f 1 = 0.067 Hz Predict the frequencies of several higher harmonics: f 6 : 0.401 Hz f 7 : 0.467 Hz f 8 : 0.534 Hz f 9 : 0.601 Hz Use the wave simulator to test each of your calculated harmonics. Note which ones appeared and which ones did not appear! f 6 - True f 7 - True f 8 - True f 9 - True Draw and label the standing waves for each of the harmonics you discovered: f 6 f 7 f 8 f 9 Discussion and Conclusions: Part A:

In conclusion, this experiment proves that it is possible to predict the harmonic frequencies of wavelengths by having at least two different frequencies for previous harmonics. This can be done by simply finding the value between the two harmonics, which was done. Then, the further harmonics discovered will be accurate. The only inaccuracies that may occur are with computational errors and slight errors when rounding off. This can be remedied by using larger decimal values instead of rounding to the nearest hundredth or so. This experiment allowed the scientist to fully understand harmonics, wavelength, tension, dampness, amplitude and all of the ways those variables interact. As stated before, this understanding can be applied to multiple fields such as technology, color theory, music and many other sciences. The knowledge gained from this experiment is invaluable and will likely prove useful in the future.

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