{"cells": [{"cell_type": "markdown", "id": "b4a3fb69", "metadata": {"tags": ["module-wave"]}, "source": ["# Attenuation\n", "[Waves](module-wave) \n", "```{index} Attenuation\n", "```\n", "\n", "In this notebook, the different types of attenuation will be discussed. Group velocity and dispersion are discussed *here* (link?).\n", "\n", "Attenuation is the loss of intensity as waves travel through a medium."]}, {"cell_type": "code", "execution_count": null, "id": "9e1b35c1", "metadata": {}, "outputs": [], "source": ["import numpy as np\n", "import matplotlib.pyplot as plt"]}, {"cell_type": "markdown", "id": "ac2c0293", "metadata": {}, "source": ["## 1. Dispersion\n", "```{index} Dispersion\n", "```\n", "\n", "In dispersion, higher frequency waves travel faster than lower frequency waves. The energy spreads out thus leaving less intensity for the pulses.\n", "\n", "
\n"]}, {"cell_type": "markdown", "id": "a5b01876", "metadata": {}, "source": ["## 2. Geometric spreading\n", "```{index} Geometric spreading\n", "```\n", "\n", "Energy spreads out as a function of area. Thus, intensity decreases away from the source. It is important to look at the dimensions of spreading, i.e. water waves pread in 2D so the area is $2\\pi r$. Body waves spread out in 3D, so the area to consider is $2 \\pi r^2$. Geometric spreading is defined as initial intensity divided by the area as a function of distance from the source so \n", "\n", "$$\\frac{I_0}{area}$$ \n", "\n", "For example, $\\frac{I_0}{2\\pi r}$ for water waves."]}, {"cell_type": "code", "execution_count": 41, "id": "9cb6b16a", "metadata": {}, "outputs": [{"data": {"image/png": 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\n", 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