(Originais Teachy 2023) - Question Hard of Physics

A physics student is studying the acoustic properties of sound tubes and decides to conduct a practical experiment to verify the resonance frequencies in an open tube and a closed tube. He starts with the open tube, which has a length L and a fundamental frequency f1. Next, he observes the second harmonic of the tube, which occurs when the column of air vibrates in two equal halves, presenting a frequency f2. For the closed tube, which has the same length L, he finds the fundamental frequency f3 and the third harmonic f4. Considering the speed of sound in the air as v=340 m/s, calculate the frequencies f1, f2, f3, and f4 for the open and closed tubes, respectively, and explain the relationship between the length of the tube and the values of the observed frequencies. Additionally, discuss how varying the length of the tube would alter the distance between the frequencies f1 and f2 in the open tube and between f3 and f4 in the closed tube, considering that the tube ends remain fixed during the experiment.