Timeline for Do all waves of any kind satisfy the principle of superposition?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2017 at 9:31 | comment | added | I.E.P. | I'm happy to help! | |
| Jan 20, 2017 at 9:17 | comment | added | user541686 | D'oh!! Of course, that makes sense... I totally didn't realize that's what you're talking about. Somehow I completely missed what you meant by your second sentence, even though it's crystal clear now in hindsight. Sorry about that and thanks for the (re-)explanation! | |
| Jan 20, 2017 at 9:08 | comment | added | I.E.P. | (cont'd) Say $f(x,t)= A\text{sin}(kx-\omega t)$, thus $df(x,t)/dx= Ak\text{cos}(kx-\omega t)$. The term $Ak$ is what is small and notice that the spatial dimensions cancel--thus rescaling space will have no effect on the governing physics of our system. | |
| Jan 20, 2017 at 9:06 | comment | added | I.E.P. | As an elementary example consider the classical derivation of the linear wave equation for a 1d string. The only way we actually yield the linear PDE is by approximating that terms of order $(df(x,t)/dx)<< 1$ (where f(x,t) is the displacement of the string at position x, time t). This is what constitutes "small oscillations." Another way of thinking of this requirement is that in this regime we are analyzing the "long wavelength" behavior of our system. | |
| Jan 20, 2017 at 8:16 | comment | added | user541686 | Could you explain the distinction between large and small amplitudes? I never understood what distinction there might exist. Can't you make any small amplitude large just by changing your units to something minuscule? How can that affect the physics? | |
| Jan 20, 2017 at 7:40 | comment | added | I.E.P. | I'm using the term "linearity" as described by the answers above. | |
| Jan 20, 2017 at 7:39 | history | answered | I.E.P. | CC BY-SA 3.0 |