I'm not sure whether this should go in the physics academic forum but to me it's more like a maths problem as I'm stuck on how to rearrange a formula so any ideas received with gratitude.
I'm reading an intro to quantum theory. At beginning of chapter it gives the equations of a standing wave in terms of trig functions (see attachment wave 1) where the symbols v=frequency of a wave lambda is the wavelength x=initial displacement of wave at time t=0.
Some pages later when taliking about the motion of an electron it solves a 2nd order differential eqtn in terms of cosine (see attachment wave2) which it says 'describes a simple sinusoidal standing wave' but I can't see how you could rearrange it to get it in a similar earlier form.
What I can rearrange it to, is the form of a travelling wave as in attachment wave 3 (equation 1.1).
Has anyone any ideas?
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Standing waves / trig problem watch
- Thread Starter
- 13-11-2005 16:22
- 14-11-2005 00:59
The reason that it's a standing wave is that it doesn't depend on time - only on space. A travelling wave is something in the form:
for some constants A, k and w. I'm not entirely sure how you manage to rearrange it to the form of a travelling wave, because you'd have to artificially introduce some time-dependence yourself!
Edit: Ahh, I see what you did! Presumably you used something like
cos(θ) = sin(θ+pi/2)
to write the cos as a sin, and you found a phase angle Ø which wasn't equal to zero. The key point is that your value of Ø would be constant - it doesn't depend on time. The form of wave given in 1.1 depends on time - they explicitly say that Ø is proportional to t.
Hope that's useful! :)
- Thread Starter
- 14-11-2005 18:43
Ok, I think I get it - haven't done physics A Level so not very familiar with the definitions of phase etc, just trying to work it out from this book I've started.