Adding waveforms, the period

[johnj7]

after doing several problems, i keep seeing that when you add the waveform of the fundamental with its higher harmonics, the period of the summed wave is equal to the period of the fundamental wave.

Could someone explain conceptually why this happens?

that would be much appreciated!

 

[Redbelly98]

Well, if the fundamental has period T, consider a harmonic with period T/N.

You can think of the harmonic also having period 2T/N, 3T/N, etc.

 

[nlightner]

I can explain the concept behind this phenomenon. The period of a wave is the time it takes for one complete cycle, or one repetition of the wave pattern, to occur. When we add waveforms, we are essentially combining two or more waves to create a new wave. The period of the new wave will depend on the individual periods of the original waves.

In the case of adding the fundamental wave with its higher harmonics, the period of the new wave will be equal to the period of the fundamental wave. This is because the higher harmonics are multiples of the fundamental frequency. For example, if the fundamental frequency has a period of 1 second, the second harmonic will have a period of 0.5 seconds, the third harmonic will have a period of 0.33 seconds, and so on. When we add these waves together, the resulting wave will have a period of 1 second, which is the same as the fundamental frequency.

This happens because the addition of waves is a linear process. This means that when we add two waves together, the resulting wave will have the same period as the individual waves. This concept is known as superposition. Essentially, the higher harmonics are adding to the original wave, but they are not changing the fundamental frequency or period.

In conclusion, when we add waveforms, the period of the summed wave will be equal to the period of the fundamental wave because of the linear nature of wave addition and the fact that the higher harmonics are multiples of the fundamental frequency. I hope this explanation helps to clarify the concept for you.