Wave amplitude as a complex number?

Question

In section 1-3 An experiment with waves of The Feynman Lectures on Physics (https://www.feynmanlectures.caltech.edu/III_01.html) it says:

"The instantaneous height of the water wave at the detector for the wave from hole 1 can be written as (the real part of) ${h_1}e^{iωt}$, where the “amplitude” $h_1$ is, in general, a complex number."

What does it mean to have a amplitude that is a complex number? I'm used to working with the wave representation of $Ae^{iwt}$ where $A$ is just a constant describing the amplitude, so I'm a bit lost when this amplitude all of a sudden is a complex number.

Buddy, as @mike stone has answered, a complex amplitude would be a complex number constant $h = a + ib$. Normally we are used to $b=0$ but the case $b≠0$ phase shifts the waveform by $\arctan (b/a)$ — Awe Kumar Jha, Dec 09 '23 at 06:47
Does this answer your question? What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$? (That question deals with waves rather than oscillations, but Emilio Pisanty's answer still applies.) — Michael Seifert, Dec 10 '23 at 15:01

score 6 · Answer 1 · answered Dec 07 '23 at 21:46

6

If $h= |h|e^{i\theta}$ then $he^{i\omega t}= |h|e^{i(\omega t +\theta)}$, so the phase is just shifted.

answered Dec 07 '23 at 21:46

mike stone

52,996

1

How does this answer the question? – Martin Argerami Dec 09 '23 at 03:09
@MartinArgerami The complex part of the amplitude just encodes a phase shift – BioPhysicist Dec 09 '23 at 19:12
@BioPhysicist: saying so in your answer would improve it a lot. – Martin Argerami Dec 09 '23 at 23:15
@MartinArgerami Well, it's not my answer, but thanks! – BioPhysicist Dec 11 '23 at 15:10
@BioPhysicist: my bad, I didn't notice it was not your answer. In any case, thanks for the clarification, which does answer the question for me. – Martin Argerami Dec 11 '23 at 16:16

Wave amplitude as a complex number?

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