When we say that square waves or rectangle waves have only one frequency, we are referring to their fundamental frequency. A square wave is a periodic waveform that alternates between two discrete levels, typically high and low, with equal durations. A rectangle wave is similar but allows for different durations of the high and low levels.
The fundamental frequency of a square wave or rectangle wave corresponds to the rate at which the waveform repeats itself. It is the lowest frequency component that, when combined with its harmonics, can recreate the shape of the waveform. The harmonics are integer multiples of the fundamental frequency.
When we add sine waves with different frequencies together, we can generate a square wave or a rectangle wave by including a fundamental frequency and its harmonics. The process of combining multiple sine waves to create a complex waveform is known as Fourier synthesis.
To generate a square wave, we start with the fundamental frequency, which corresponds to the rate at which the waveform repeats. This fundamental frequency sine wave has an amplitude that represents the high level of the square wave. We then add odd harmonics (3rd harmonic, 5th harmonic, 7th harmonic, etc.) with decreasing amplitudes. Each harmonic contributes to the sharp transitions or "edges" of the square wave. As we add more harmonics, the square wave approximation becomes closer to the ideal square wave.
A similar process applies to generating a rectangle wave, where the durations of the high and low levels are different. The fundamental frequency still corresponds to the rate at which the waveform repeats, but now we introduce the odd harmonics with different amplitudes to shape the varying durations of the high and low levels.
By carefully selecting the amplitudes and phases of the sine waves at different frequencies, we can approximate a square wave or a rectangle wave with greater accuracy.
In summary, square waves and rectangle waves have one fundamental frequency, which is the lowest frequency component that, along with its harmonics, can reproduce the shape of the waveform. The inclusion of harmonics allows for the sharp transitions and varying durations in the case of rectangle waves.