- #1
NutriGrainKiller
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This is for Optics - the third calc-based physics class I've taken. I'm taking calc4 now and this class seems to use differential equations quite frequently..something i am just now learning. This is an example problem that i don't quite understand:
now, the book attempts to explain the solution in the back of the book, but i don't quite get it. it says both a) and b) are waves since they are twice differentiable functions of (z-vt) and (x+vt) respectively. Therefore, for a) psi = a^2(z - bt/a)^2 and the velocity is b/a in the positive z-direction. For b) psi = a^2(x + bt/a + c/a)^2 and the velocity is b/a in the negative x-direction.
i don't understand where the bolded equations come from. I understand how they got the velocity and direction from those equations, but no idea how they were derived.
Which of the following expressions correspond to traveling waves? For each of those, what is the speed of the wave? The quantities a, b, and c are positive constants.
a) psi(z,t) = (az - bt)^2
b) psi(x,t) = (ax + bt + c)^2
c) psi(x,t) = 1/(ax^2 + b)
now, the book attempts to explain the solution in the back of the book, but i don't quite get it. it says both a) and b) are waves since they are twice differentiable functions of (z-vt) and (x+vt) respectively. Therefore, for a) psi = a^2(z - bt/a)^2 and the velocity is b/a in the positive z-direction. For b) psi = a^2(x + bt/a + c/a)^2 and the velocity is b/a in the negative x-direction.
i don't understand where the bolded equations come from. I understand how they got the velocity and direction from those equations, but no idea how they were derived.