Harmonics and Integer Multiples

[Becca7644]

Homework Statement

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So, this is a question I have in one of my assignments and I'm really going round in circles with it. Any pointers or links to additional reading would be gratefully received! This is a pass criteria question on a General Engineering HNC.

Homework Equations

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Why do component harmonics occur at integer multiples of the fundamental frequency in any periodic waveform?

The Attempt at a Solution

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I know my answer doesn't answer the question, but it's the best I can come up with ...

Component harmonics occur at integer multiples of the fundamental frequency as all harmonics associated with periodic waveforms have to be an exact multiple of the ground frequency, so that they start a new cycle when the fundamental starts a new cycle.

Analysing harmonics by calculating the magnitude and phases of the fundamental periodic waveform is known as the Fourier series. This allows us to establish the relationship between a function in the domain of time and a function in the domain of frequency. Fouriers theorem states the every non sinusoidal periodic wave can be decomposed as the sum of the sine wave through the application of the Fourier series.

I was then going to go on and talk about static waves.

Any guidance would be appreciated.

Thanks in advance.

 

[DrClaude]

Why is there a particular fundamental frequency to start with?

 

[Becca7644]

Why is there a particular fundamental frequency to start with?

Thanks for the pointer.

Because the fundamental is created by a sinewave generator, and because the sinewave generator doesn't produce an ideal (pure sinusoidal) sinewave, harmonics are produced. The frequencies of the harmonics are integer multiples of the fundamental (2f, 3f, 4f) ?

 

[DrClaude]

As this is a question about engineering, I was thinking more about vibrations. I now see that the question mentions "periodic waveforms."

The answer can be the same in both cases. It boils down to boundary conditions. As you said in the OP, the periodicity constrains which frequencies can be present. I would probably elaborate more on why that is when answering such a question.

 

[Becca7644]

As this is a question about engineering, I was thinking more about vibrations. I now see that the question mentions "periodic waveforms."

The answer can be the same in both cases. It boils down to boundary conditions. As you said in the OP, the periodicity constrains which frequencies can be present. I would probably elaborate more on why that is when answering such a question.

Thank you. I appreciate your help!