The discussion revolves around the behavior of standing waves on a string fixed at both ends under tension. Key points include the relationship between the length of the string and the wavelength, where the fundamental frequency is determined by the equation f = v/(2L), indicating that increasing the length decreases the frequency and vice versa. The amplitude of the wave does not affect the fundamental frequency, which remains constant regardless of changes in amplitude. Additionally, increasing the tension in the string results in an increased fundamental frequency due to the relationship between tension and wave speed. Overall, the participants worked through the equations to clarify misconceptions and arrive at the correct answers for the homework questions.