Final answer:
Removing the first harmonic, or fundamental frequency, from a tone's waveform does not change the repetition rate but alters the sound quality and timbre. The first overtone is actually the second harmonic, not the first. Harmonics define the multiples of the fundamental frequency and are crucial in the formation of sound quality.
Step-by-step explanation:
When a tone's waveform is altered by removing the first harmonic, this fundamentally changes the sonic characteristics of that tone. The first harmonic is synonymous with the fundamental frequency, which is the lowest frequency of vibration of a standing wave. Since harmonics are all multiples of the fundamental frequency, removal of this component can significantly change the sound's quality and timbre. The repetition rate, or frequency, of the waveform will remain the same because it is determined by the fundamental frequency which, by definition, is the first harmonic itself. If the first harmonic is removed, the sound would be left with higher harmonics which might not be as perceptible or may result in a sound with a different perceived pitch and timbre. It is important to note that the first overtone is actually the second harmonic, not the first, which is a common misunderstanding.
The first overtone, or second harmonic, is the next frequency above the fundamental frequency that can produce a standing wave on a string or in an air column. It is the second simplest mode of vibration after the fundamental frequency. Consequently, there is a correction to be made: the standing wave patterns known as the normal modes highlight that the first normal mode is the fundamental frequency (first harmonic) and the second mode is the first overtone (second harmonic).