- #1
Quadrat
- 62
- 1
Homework Statement
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I found a couple of assignements for a physics course I will take later this year- so I started looking into them a bit in advance. It concerns wavefunctions. I'm a bit rusty on my trigonometric identities So I would love if someone could try to help me solve these two questions:
1) ##g(x±vt)## and ##h(x±vt)## are differentiable twice. Show that ##y(x,t)= Ag(x±vt) + Bh(x±vt)## is a solution to the wave equation where ##A## and ##B## are constants and ##v## is the speed of the wave.
2) Which of these functions ##(y(x,t))## is/are a solution(s) to the wave equation. If so- which direction does the wave propogate?
a) ## y = A(x^2-v^2t^2+2vtx)##
b) ## y = A(x^2+v^2t^2+2vtx)##
c) ## y= Acos(kx-ωt)##
d) ## y = Acos(kx-ωt)- Acos(kx+ωt)##
Homework Equations
The wave equation looks like this: ##\frac{{\partial ^2 y}}{{\partial x^2 }} = \frac{1}{{v^2 }}\frac{{\partial ^2 y}}{{\partial t^2 }}## If the functions in ##2## satisfy the wave equation then both sides should be equal.
I know if I get something that has the form (kx-ωt) in the function it will propogate in the positive x-direction. And (kx+ωt) then it will propogate in the negative x-direction.
The Attempt at a Solution
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The only one I know for certain to be a solution to the wave equation is c, and that would travel in the positive x-direction. I'm pretty sure that that's not the only one, so how would one go about solving these kinds of questions? I'm hoping to get a good grade when this course is due so I want to get started soon since my trigonometric knowledge is a bit rusty. The first question is confusing for me. Useful tips and/or links for reading/videos/lectures are welcome!
Thanks for reading.