What is the relationship between the speed on the electromagnetic wave and the density of the medium in which the electromagnetic wave travel through?
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2This is really a duplicate of several existing questions e.g. Relation between density and refractive index of medium and Why does the light travel slower in denser medium?, but I don't think any of the duplicates have a nice clean answer. – John Rennie Jan 02 '15 at 16:54
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You mean the optical density? Sometimes we use "optical density" to talk about "index of refraction" usually denoted by $n$. In that case (and only in that case), can the speed of the wave inside the medium be calculated as $c_{medium}=c_{vacuum}/n_{medium}$. – CuriousOne Jan 02 '15 at 16:55
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No, I mean the density of the medium (the mass in a given volume). – Lilly Jan 02 '15 at 17:42
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Well, in that case, there is no relationship. All that matters is the optical density, or the equivalent (which has other terms) for extremely low-frequency EM waves. – Carl Witthoft Jan 02 '15 at 17:45
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If the waves have a low enough frequency and the medium is composed of an ionized gas (e.g., the solar wind), then there are several relationships between the wave speed and ambient density known as dispersion relations. – honeste_vivere Jan 04 '15 at 17:36