Final answer:
Removing the first overtone, which is the second harmonic, changes a tone's waveform by altering its tone quality or timbre, but it doesn't change the fundamental frequency or repetition rate of the waveform. The concept of harmonics is related to simple harmonic motion, where frequency is independent of amplitude.
Step-by-step explanation:
The question revolves around the concept that harmonics are integral multiples of the fundamental frequency in sound waves. Here, the statement 'Removing the first harmonic changes a tone's waveform but not its repetition rate' could be a little confusing. The term 'first harmonic' actually refers to the fundamental frequency itself, which is the lowest frequency of a periodic waveform. Removal of the fundamental frequency would drastically alter the sound's characteristics.
Nevertheless, the statement might instead be referring to the removal of the 'first overtone', which is the second harmonic and does not affect the repetition rate, or the fundamental frequency, of the waveform. Sound is a wave motion, and when the first overtone is removed from a tone's waveform, it alters the wave's shape and consequently changes the tone quality or timbre, but the fundamental frequency or repetition rate of the tone remains unchanged.
This is consistent with the physics of simple harmonic motion (SHM) where the period (T) and frequency (f) of a simple harmonic oscillator, such as a guitar string, are independent of its amplitude. This means that removing higher harmonics or overtones doesn't affect the original frequency of the vibrating string, which corresponds to the fundamental frequency or first harmonic.