Dividing the Audible Range

Dividing the Audible Range

  1. Tenson
    The way sound behaves in an enclosed space changes drastically depending on its frequency, or more precisely its wavelength, and the size of the room. We can divide the range in to 4 areas consisting of the Pressure Zone at ultra-low frequencies, the Modal Range at low frequencies, the Transitional (A.K.A. Diffuse) Range at mid frequencies and the Specular Range at high frequencies.


    We can roughly define these ranges by the following rules.

    A = The Pressure Range is below, and the Modal Range is above the frequency where half a wavelength fits between the furthest apart room boundaries.

    B = The Transitional Range begins from the top of the modal range, approximately defined by the equation: F ≥ 11250 (√RT60 / Room Volume)

    C = The Specular Range starts at approximately 4 times the beginning frequency of the transitional range.

    The image above also shows roughly the affect of those ranges on the response of a speaker with a flat response in a free-field enviroment.

    In the Pressure range of frequencies, the wavelength of sound is so large that not even half a cycle can fit in the space between the room boundaries. The pressure level of the whole enclosed space thus rises and falls at the frequency of the sound wave. The wavelength is also so large that no object in the room is likely to obstruct it's path, it will simply pass right through it. The result of this behaviour is two-fold. The ultra-low frequency sound is boosted compared with a completely open space. That's not surprising, because a speaker can't pressurize the entire outside world. Also, the response is very even and smooth since the wave doesn't reflect from the room boundaries out of time (phase) with the source.


    Next up is the Modal range, where more than half a wave will fit between the boundaries. When sound behaves like this we find some frequency of waves fit perfectly between the room boundaries. When the waves reflect back in the opposite direction they add with the original and create a stronger sound that takes a long time to decay, however this created wave does not seem to travel along in a specific direction like a normal wave, it stands still. This creates static areas of high sound levels in one area of the room (between the numbered points on the animation below), and low sound levels in others (exactly on the numbered points in the image below).

    If the waves don't fit neatly between the rooms boundaries then they don't get this boost, the sound remains at it's weaker 'natural' level and also decays quicker. The wavelengths in this range are large enough that they will bend around and encompass nearly any object in their path (table, chair, person), only something very big and dense like a wall will cause reflection.

    Boundary Reflection


    Standing Wave Formation


    Animations taken from http://physics.usask.ca/~hirose/ep225/animation/reflection/anim-reflection.htm

    I'm now going to skip the Transitional Diffuse Range and go directly to the high frequency Specular Range. In the Specular range, the wavelength of sound is too small to effectively bounce back and forward between room boundaries. Large waves think the wall is flat, but even a small surface bump can cause high frequency specular waves to shoot off in a different direction. In this range we can cite the rule 'the angle of incidence equals the angle of reflection'. That means whatever angle the wave hits a surface, it will reflect off in the opposite direction. So, in an enclosed space with a sound source, we find the sound comes not only directly from the speaker to the receiver, it is also followed by many slightly quieter copies of the sound which took longer paths sound the room reflecting off surfaces.


    So lets take a step back and look at the Transitional Diffuse Range now. These wavelengths are large enough that they don't directly reflect from every object in their path, yet they also can not bend right around it. What we find is the wave splits, making multiple level reduced copies of itself. Some partly bend around the obstacle, while others reflect. This is called diffraction; when a single wave is made to split and travel multiple different directions. You may also hear the term Diffusion. This is when a wave is split roughly equally in all directions.