Plane Waves

Tags: #physics #plane waves

Equation

$$u(\vec{x},t)=2^n\hat{u}\cos(\omega t)\sum_{i=1}^n\sin(k_ix_i) \\ u(\vec{x},t)=\hat{u}\cos(\vec{k}\cdot\vec{x}\pm\omega t+\varphi) \\ \frac{f}{f_0}=\frac{v_{\rm f}-v_{\rm obs}}{v_{\rm f}}$$

Latex Code

                                 u(\vec{x},t)=2^n\hat{u}\cos(\omega t)\sum_{i=1}^n\sin(k_ix_i) \\
            u(\vec{x},t)=\hat{u}\cos(\vec{k}\cdot\vec{x}\pm\omega t+\varphi) \\
            \frac{f}{f_0}=\frac{v_{\rm f}-v_{\rm obs}}{v_{\rm f}}

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Introduction

Equation



Latex Code

            u(\vec{x},t)=2^n\hat{u}\cos(\omega t)\sum_{i=1}^n\sin(k_ix_i) \\
            u(\vec{x},t)=\hat{u}\cos(\vec{k}\cdot\vec{x}\pm\omega t+\varphi) \\
            \frac{f}{f_0}=\frac{v_{\rm f}-v_{\rm obs}}{v_{\rm f}}

Explanation

Latex code for the harmonic oscillations. I will briefly introduce the notations in this formulation.

  • : harmonic plane wave is defined as u(x,t)
  • : Doppler effect

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