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Sound reflections.

Imagine a sound source in open field, as in an open meadow: The sound emanates from the source spherically in all directions.
The direct sound source moves then before you, and never returns.

Now consider the same source in a room: The direct sound is moving ahead, but when it strikes a wall this sound is reflected.
In this case, the direct sound moves past you using a direct path, and will return in many times and many reflected path, until it disappears considering energy's.

A sound comprising many sound reflections is totally different comparing sound in an open field. Reflections convey important information about the room size, shape and composition of these walls.
Reflections define the sound characteristics of a room.

 

 

a- a- Specular reflection:

The mechanism of reflection from a plane surface is simple. This figure shows the reflection of wavefront on a rigid and flat surface.
The spherical wave front strikes the wall, and the reflected wave fronts are returned toward the source.
This is called specular reflection and behaves the same as light reflection from a mirror, described by Snell-Decartes 's law.

The sound follows the same rule as the light: the angle of incidence is equal to the angle of reflection, like an image in a mirror; the reflected sound acts as if it came from a virtual sound image. The virtual source is located behind the acoustically reflective surface, such as viewing an image in a mirror. This image is at the same distance behind the wall that the real source from the wall.
This is the simple case of a single reflecting surface.
When sound strikes many surfaces, multiple reflections will be created.
Take the example of two parallel walls as indicated on the figure below.

The sound source will strike the left wall, which can be modelled as a virtual source "I 1" (first order).
The sound continues to reflect back and forth between the parallel walls creating a virtual source of the virtual source, "I2" (second order).
Several images of images appear (3rd order, 4th, etc ...) until the total loss of sound energy and thus its disappearance.

We observe that in this example, the walls are separated by 15 units of distance, so the first order images are separated by 30 units, the second order images ares 60 units apart, the third order images are separated by 90 units, and so on. With this modelling technique, we can ignore the presence of walls, and consider the sound as coming from many sources apart from the virtual real source, arriving with delays based on their distance from the source. In a rectangular room, there are six surfaces and the source has an image in all six surfaces, sending energy back to the receiver, resulting in a very complex sound field.
When we calculate the total sound intensity at a given receiving point of this room, the contribution of all these images will be taken into consideration.