Other sound-on-nature characteristic is the reflection it produces on its surroundings, filling the air with bouncing signals that are perceived as early and late reverberation, giving sound to the ears on a [discrete] time structure, related to the place we are at.

Much information is conveyed through sound’s reflections about the material, geometry and space the listening environment is embed in. Sound can carry a metal voice when reflected on such material or a void echo when bouncing on a hollow chamber.

Models can be created to simulate the scattering sound of reflections on real circumstances.  They basically consist on sound repetitions with decreased amplitude and altered frequency response.

Although there are sophisticated models and software devoted to compute the accurate sound scattering on a given environment, considering a complex array of factors, such as reflection coefficient on materials used on the walls etc., a simpler model is used to synthesize some location’s reverberation, like the Schroeder reverb  (Kemp, 2011), when the accuracy of the reflection is not the main goal of the rendering. And what is more, most of the time, simple reverb models are available that are more complex than current artists/musicians are aware of.

So, instead of creating a sophisticated model of a concert hall, the common practice is to create a shoebox room, and the sound reflections are considered to behave as light reflecting on mirrors, refracting and reflecting. Refraction is simulated by multiplying the incident sound to a constant value corresponding to the material’s reflection coefficient, such that:

Equation 4

Where g is the gain after the sound has been reflected on a surface with absorption coefficient equal to a.

The frequency response of the reflection of the sound on a certain material is modeled using frequency domain filters. These account for the effect of materials on the listening area and the filtering effect of the air on which the sound is traveling.

The shoebox model is a commonly used one when creating synthetic reverb, with which it is easy to create an Image Source reverb algorithm  (Kemp, ImageSource, 2011) that calculates possible paths that sound follows if reflecting on a geometrical fashion (just as light does) in order to arrive at the listener’s ears. One can then calculate the first n reflections out of infinity of possibilities and render a convincing 3D reverb effect. This method measures the distance the sound would need to travel before making its way to the head, and based on that timing, the air filtering is performed, and the time and level differences are calculated.

Further attention is focused on how the sound interacts with the location, when it ceases, leaving a characteristic tail, related to the reflections properties of the reverberation phenomenon, referred to as Decay Time, which is the time it takes to the sound to decay by 60 dB.

The Spatialization presented here uses this shoebox model to generate the timing of the impulses arriving at the head, the absorption coefficients are considered with the expression shown above so that the sound is attenuated depending on how many times it has bounced on the walls. This model induces time and level domain reverbs, and shelf filtering is added to emulate the frequency response of the reflections on the walls. Finally, a 2nd order Butterworth filter acts as the effect air has on the sound when traveling long distances before being heard (Peters, ViMiC, 2009). Late reverb on the ViMiC modules is built with a feedback delay network

Further on this chapter: