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Why high frequencies are directional and low aren't?

When discussing good sounding rooms, I wrote about reflections, and mentioned that low frequencies are omnidirectional while highs are directional (and as a consequence, it's easier to absorb the latter than the former, for the simple reasons that you can tell where they end up on the wall!).


In other terms, low frequencies are spherical (looking down from the ceiling, you would draw them as circles emitting from the source), while high frequencies are planar (i.e. looking down from the ceiling, you would see them as parallel lines emitting from the source).


But why is that so?



First off: I lied.


All sound waves are spherical.


What allows us to think of some as spherical and some other as planar is the relationship between the size of the room we're in, and the source, with respect to the wavelength of the frequency we're looking at.


It's simple to understand using an analogy we all are familiar with: planet Earth.


Now, unless you are part of questionable circles or have grown up in some jungle in Papua-New Guinea (but then, how are you reading this blog?), it should be fairly clear to you that the Earth is (give or take) a sphere.


And yet when you walk a road, it feels perfectly flat, you have absolutely no sense of curvature.


Why?


Simple: Earth's is immense with respect to the distance you are walking - your size. In particular, Earth's diameter on the equator (a linear measure, that you can describe in kilometers or miles) is about 12.000 Km/7457 miles, way longer than the say 30 Km/18 miles that a trained walker can make in a day.


So from the perspective of your size, Earth curvature is about 12.5 cm every 1 Km (or 8 inches every 1 mile). At the meter scale, where we live, that's about 0.0125 cm every meter, that is a tenth of a micrometer per meter - where a hair's width is about 17 to 180 micrometers, that is to say 100 times higher.


In the scale we can perceive the physical world, the curvature is imperceptible, so we can happily consider the road flat - which works fine so long we stay within a meter-scale situation.


The same happens with sound waves: a room is usually a volume at the single meter scale or ten-feet scale. Sources are a loudspeaker or a mouth or something at that scale. High frequency sound waves are high frequency because they repeat many times in one second. A 10 KHz waves repeats 10.000 times in a second. Since sound speed is 343 m/s at room temperature, that means that each air oscillation is very short: 0.1126 feet or 0.03432 meters.


The scale of the wave is so much smaller than the scale of the room and the source, that (exactly as for our human scale with the scale of Earth) we can consider it flat (and hence directional).



Or in other words: from our point of view, in order to "see" the wavelength, we have to "zoom in" very very much - at that scale, the walls become incredibly far away and therefore the part of spherical wave that we can see can be treated as planar.


On the other side, low frequencies waves are absolutely comparable with the size of a source and a room's walls (and even larger) : the wavelength of and 80Hz sound is 14.075 feet or 4.29 meters. A 20 Hz sound's wavelength is much longer than most rooms wall (unless you live in a castle), at 17.16 meters or 56.3 feet.


In that situation, the scales of source, room and wavelength are absolutely comparable and therefore, we can't ignore the fact that the sound wave is actually curved (a sphere) and not planar.


There you have it. This is why we can treat sound waves whose length is much smaller than the source and room as planar and directional, but waves whose length is in the same need to be considered as spherical and omnidirectional.



The obvious consequence of this is, of course, where you place your absorption material for room treatment.


But there are other, less immediate - and we'll look at them soon in post about why certain microphone sound "better" than others.

Good recordings!



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