Timeline for Are monochromatic EM waves supposed to be sinusoidal?
Current License: CC BY-SA 4.0
6 events
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| Jun 2, 2020 at 16:50 | comment | added | Claudio Saspinski | I understood your point. The advantage of choosing a standard function like sine/cosine is that $k$ is the only parameter to specify wave length and frequency, (if the wave speed is a constant what is the case for EM). And it is suitable for man made radio waves, that are sinusoidal by construction. The disadvantage is the need to use all the Fourier analysis machinery to represent a simple pulse function as my example, common from light emitting sources. | |
| Jun 2, 2020 at 10:10 | comment | added | nanoman | @ClaudioSaspinski The exact same pulse can be written with a different $k$, without changing how localized it is. If it's $(R^2 - u^2)^{1/2}$ with a given $k = k_1$, then it's also $(R^2 - 4u^2)^{1/2}$ with $k = k_1/2$, etc. Given your definition of $f$ as an arbitrary function, there's no way to examine a physical wave (dependence on $x$ and $t$) and decide what its $k$ value is. That's why I'm objecting to the apparent premise of your question, that it's even possible to meaningfully define "monochromatic" without restricting $f$. | |
| Jun 1, 2020 at 22:37 | comment | added | Claudio Saspinski | Of course it can be written in that form for any $k$. In my example, it is easy to see that $k$ is related to the spread of the pulse. Bigger $k$ means more localized. | |
| Jun 1, 2020 at 21:59 | comment | added | nanoman | @ClaudioSaspinski I think you are restating my point. There is no meaning to talking about a wave composed of $f(k(x - ct))$ "with a narrow range of $k$" (or a single $k$), because $k$ is not an observable property of such a function. Any plane wave (including a pulse) can be written in that form for any $k$ by suitably defining $f$. You have to specify $f$ more strictly in order to give meaning to $k$. | |
| Jun 1, 2020 at 21:20 | comment | added | Claudio Saspinski | When I say $f(u)$ where $u = k(x-ct$), it means some function. It can be $sin(u)$, but also $(R^2 - u^2)^{1/2}$ for some k and R. Note that it is not necessary for f to be periodic to solve the wave equation. It can be a pulse travelling at light speed. | |
| Jun 1, 2020 at 20:44 | history | answered | nanoman | CC BY-SA 4.0 |