da_willem said:If you express a wave as a Fourier series like:
[tex]z(x,t)= \sum _{n=1} ^{ inf.} A_n cos(nk_0 x - \omega (n) t )[/tex]
Then what is the physical interpretation of a non-zero imaginary part of a component amplitude?
da_willem said:I read your word document, and would like to thank you very much for that. But maybe I should have specified my question some more, it is still not very clear to me...
If you want to describe a real wave in a formula you give it's height as a function of position and time. A height cannot be imaginary. So when an imaginary component amplitude appears in you Fourier representation of that wave there must be somethig wrong. This component cannot be canceled by another component can it? Is the appearance of an imaginary component in the sum a mathematical curiosity, or does it simply never appear for a real signal, or...?
Imaginary FS components refer to fictional or hypothetical elements that are used in scientific models or theories to represent a concept or phenomenon. They do not exist in the physical world but are used as a tool for understanding and explaining complex ideas.
Imaginary FS components are used in science to simplify complex concepts and make them easier to understand. They can also be used to test theories and make predictions about real-world phenomena.
Imaginary FS components are not considered reliable in scientific research as they are not based on empirical evidence. They are used as a tool for understanding and exploring ideas, but they cannot be used as evidence to support a hypothesis or theory.
Since imaginary FS components are not based on empirical evidence, they cannot be proven or disproven. However, they can be useful in developing and testing theories, which can then be supported or refuted by real-world evidence.
One potential drawback of using imaginary FS components is that they may oversimplify complex concepts and lead to incorrect assumptions or conclusions. It is important for scientists to be aware of the limitations of using imaginary components and to validate their findings with real-world data.