# Tagged Questions

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2answers
148 views

### Energy stored in space/frequency electric field

I've come across a problem with finding the energy stored in time/frequency electric field. In space/time we have (taking $\epsilon = 1$)  Energy = \frac{1}{2} \int_V |\mathbf{E}(\mathbf{x},t)|^2 ...
1answer
140 views

### What's the average position of oscillating particles in a box with periodic boundary conditions?

Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D). Now put a ...
1answer
36 views

### Why pulse waves results in wave packets?

I was doing experiments of measuring sonic velocity and I generate pulse waves from sensor 1, but when they are received by sensor 2, I saw wave packets on the oscilloscope, can you explain why? I was ...
0answers
97 views

### Discrete sum over an exponential with imaginary argument, considering only every second lattice site?

Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g., A-A-A-...-A-A (total of N sites) ...
0answers
46 views

### Fourier Transform of ribbon's beam Electric Field

I have a monochromatic ribbon beam with $E(x)e^{i(kz-\omega t)}$ being the electric field's amplitude. I want to show that the lowest order approximation in terms of plane waves is ...
0answers
147 views

### Splitting light into colors, mathematical expression (fourier transforms)

I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function $G(x)$ of photons hitting a certain area to include just ...
0answers
51 views

### Definition of frequency domain coordinates

I am using the Fourier Transform in Optics to perform differentiation with a filter by making use of the relation \$\frac {\partial}{\partial x} f(x)=2\pi i \int^{\infty}_{-\infty} u F(u) \exp (2i\pi ...
0answers
53 views

### How to solve following equation (Yukawa field)?

By using Lagrangian for Yukawa interaction,  L = -\frac{1}{c}A_{\alpha}j^{\alpha} + \frac{1}{8 \pi c}(\partial_{\alpha}A_{\beta})(\partial^{\alpha}A^{\beta}) + ...
0answers
89 views

### What should the amplitude be when plotting 1-sided Amplitude Spectrum?

I have a continuous signal $x(t)$ such that $$x(t)=12\cos(6\pi t)+6\cos(24\pi t)+3\cos(30 \pi t)$$ and is asked to sketch a 1-sided Amplitude Spectrum of the signal $x(t)$ if sampled above the ...
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