Technical PS: Snow

Author’s note — Teena might or might not think to ask, “Well, why does snow trap sound but it doesn’t trap light?” but an alert classroom student almost certainly will. I didn’t see a satisfactory way to explain that to a seven-year-old without going down a stack of “Why?” rabbit holes she’s not ready for. There’s some good Physics here, though, and just in case any of my classroom teacher readers have the same question…

It’s all a matter of how efficiently wave energy dissipates into the absorber. That in turn depends on the nature of the wave-absorber interaction and the wave’s parameters.

Lightwaves are electromagnetic so they interact with the absorber’s charged components. In particular, visible light’s primary mode of absorption is with the absorber’s electrons. In a visible light interaction, the photon raises an electron to a higher-energy state. That only happens if the photon’s energy exactly matches the difference between a lower and higher quantum state within the absorber’s molecules. Any photons that don’t match simply pass by, which is why pure liquid water is transparent and colorless — water molecules have no significant electronic transitions in the visible range.

If a photon is absorbed, there are several pathways back down to a lower state. The most likely pathway is simply to re-emit a photon of exactly the same energy that the incoming photon had (no net energy absorption). Most of the other pathways eventually lead to energy dissipation via random molecular motion, that is, heat.

Bottom line: most of light’s energy isn’t absorbed by snow, dissipation efficiency is very low, and most of the light escapes.

Soundwaves are kinetic, just push-pull forces acting on entire bodies (molecules, crystallites, etc.). There’s virtually no quantum “filtration” — essentially all of the energy is eligible for absorption. Freshly-fallen snowflakes are only weakly bound together so each of them can absorb vibrational energy from a passing wave. (Unless it’s “wet” snow falling at freezing temperature — those crystals weld together to become solid ice too quickly to be a good sound absorber.) Bottom line: snow exhibits very high sound wave dissipation efficiency.

The other factor is the combination of wavelength and wave velocity. Together they control the duration of the absorber’s interaction with one cycle of the wave. Visible lightwaves are about 500 nanometers, give or take a factor of 2, and travel at 3×108 meters/sec. An absorber has only (500×109 / 3×108) = 1.7×1015 seconds to interact with that wave. That’s a tenth to a hundredth of typical times for molecular vibrations so energy transfer isn’t very effective. Result: even lower dissipation efficiency.

Contrast that with soundwaves. Speed of sound in air is about 343 meters/second, and waves in a piano’s range (for instance) goes from A0 (12.5 meters peak-to-peak) to C8 (0.082 meters or 82 centimeters). The corresponding peak-to-peak interaction times (exercise for the reader) are roughly 1012 times longer than molecular vibration times — lots of opportunity for a molecule to grab some vibratory kinetic energy from the wave. Result: even higher dissipation efficiency.

So, snowfall is quiet because sound energy is absorbed very efficiently in the many spaces in between those spiky crystallites. By contrast, new-fallen snow is bright because light isn’t absorbed but rather is reflected or transmitted by refraction. New-fallen snow is white because refracted spectra are quickly re-combined by further refractions.

~~ RO

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