The student had successfully focused the essay on the analysis of both primary and secondary sources, employing primary sources like the wave equation and the Fourier Series, alongside scholarly articles to support theoretical concepts in music theory. The title, "Vibrating Strings and Musical Theory of Harmonics," effectively conveys the investigation's topic and aligns with the research question, which clearly states the mathematical techniques applied. The student provided necessary explanations of the title and outlined the mathematical areas explored, maintaining clarity and focus throughout the essay. Furthermore, the research question emphasizes the application of the Fourier Series, while the essay was structured logically, with coherent sections that build on one another, enhancing the overall analysis.