Final answer:
When you add the first harmonic to the higher harmonics, you create a complex sound wave with a combination of frequencies, resulting in a richer sound. The overtones are sequential multiples of the fundamental frequency.
Step-by-step explanation:
Adding the first harmonic and the higher harmonics results in complex sound waves with a richer timbre due to the combination of multiple frequencies. The first harmonic is the fundamental frequency and the simplest sound wave, while higher harmonics are multiples of that fundamental frequency. For example, in a tube closed at one end, we refer to the first overtone as the third harmonic because the frequency of the first overtone is three times the fundamental frequency (f' = 3f).
The pattern of resonances, where the fundamental frequency is the first harmonic and the overtones are the higher harmonics, continues sequentially. The second overtone would be the fifth harmonic, and this pattern defines the resonant frequencies in acoustical systems such as musical instruments and air columns.