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GR8677 #4
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Alternate Solutions |
syreen
2013-09-23 20:27:12 | the argument looks like a traveling wave sin(wt-kx) where w=1/T, k=1/lamda. Know that vphase=w/k and so w/k=lamda/T |  |
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Comments |
casseverhart13
2019-09-17 03:26:45 | It was nice of you to provide this timely problem - just what I needed. click here |  | ernest21
2019-08-10 03:09:39 | But, to be consistent, I think the and should each lose the power? twoplustwo forum | | fredluis
2019-08-08 12:50:11 | Tried get rid of it, too, but it seems that you can\'t edit even your own posts. oh well. carpet cleaner | | joshuaprice153
2019-08-08 05:07:58 | Thanks for the information on this. I really enjoy the write-up. tree pruning | | syreen
2013-09-23 20:27:12 | the argument looks like a traveling wave sin(wt-kx) where w=1/T, k=1/lamda. Know that vphase=w/k and so w/k=lamda/T | | Prologue
2009-10-12 08:38:10 | I think the explanation for B needs to be spelled out a little better. The wave looks the same in 'some reference frame traveling through space' no matter what time it is. This means you need to find a relationship between x and t such that the argument for sine gives a constant output through all time for the same x' - where x' is not the velocity but the space coordinate in the new moving frame. We need to find a  such that ![\frac{d[sin(x')]}{dt}=0](/cgi-bin/mimetex.cgi?\frac{d[sin(x')]}{dt}=0) . If you want this to be independent of time then that means the argument has to be constant with respect to time. So =constant=C) . Now you can solve for x to get ) . Now you have the time dependence for x and you can just take the time derivative to get  .
I know this is long winded but these little details might be nice for someone that isn't comfortable with shifting.
Prologue
2009-10-12 10:54:45 |
That ![\frac{d[sin(x')]}{dt}](/cgi-bin/mimetex.cgi?\frac{d[sin(x')]}{dt}) should logically be a ![\frac{d[sin(\frac{2 \pi}{\lambda}x')]}{dt}](/cgi-bin/mimetex.cgi?\frac{d[sin(\frac{2 \pi}{\lambda}x')]}{dt}) but it doesn't change the rest of the post at all.
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| | anmuhich
2009-03-19 08:39:59 | Or you just know that for a sine wave the velocity is just the wavelength over the period. | | icelevistus
2007-09-27 16:29:19 | The only variables/constants we can assume the units of are x and t. All others are unspecified, despite what convention suggests.
Thus, the application of dimensional analysis for eliminating answers only works for D.
icelevistus
2007-09-27 16:30:20 |
Never mind, the units are implicit for the sin argument to be unitless.
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