# REFLECTION

## REFLECTION

When the sound wave reaches the boundary of the medium in which it is distributed, can occur more than one process.

Part of the sound is reflected. In this reflection the angle of incidence equals the angle of reflection.

On the chart
is the angle of incidence, and

– of reflection.

The line perpendicular to the line of separation of the two circles is called normal. The angles of incidence and reflection are measured against it.

The normal is the imaginary line or vector. which is perpendicular to the surface of am object. In our case this is the border between two environments:

The energy of the sound wave when it reaches the boundary of a new environment can be transformed in several directions.

First, it is a reflection.

It depends on the the reflection factor of the surface reached by the wave.

The reflection can be mirrored or diffuse depending upon the nature of the surface and its micropores.

Secondly we have absorption. Part of the sound energy is absorbed in the transition to the new environment. In practice, this is a heat loss caused by frictional resistance of the material of the the new environment, which is presumed to be of higher density than that of air. Sound absorption coefficient is different for different materials and is dependent on the frequency, ie sound absorbing surfaces are non-linear with respect to frequency of the absorbed sound energy from them.  This ratio generally increases with increasing the frequency. For this reason, sound absorbing panels are usually most effective in the high and partly in the mid frequencies. This is the reason in many cases they can not provide the frequency linearity of the room in which they are placed. Therefore usually we apply other acoustic techniques to neutralize the low frequency waves when necessary.

The third consequence of reaching a sound wave to another environment is passing through it. We call it transmission of transition.

Part of the energy goes into the new environment, thus it is lost from the former. Typically, both traces are of varying density and, therefore, the speed of sound is changed by entering a new environment.
This phenomenon we call refraction. It happened when the wave travels from one environment  to another, changing its speed because the different density of the two environments.

In this situation, if the wave does not attack  border between the two environments exactly perpendicularand angled sound front enters differently in the new environment with different speeds and therefore changes its direction.

The three coefficients – reflection, absorption and transition – have a total 1.

None of them, except in absolutely ideal conditions, can not be equal to 1, the value is always less than 1.

Let us now consider the three types of processes separately.

## reflection

Based on a graph, we can formulate the following relations:

1. The incident ray, the reflected ray and the normal to the reflection surface at the point of the incidence lie in the same plane.
2. The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal.
3. The reflected ray and the incident ray are on the opposite sides of the normal.

Because of sound absorption to some extent in reaching the new environment only part of it is reflected back as a wave. The reflected wave is always less than the incident amplitude and phase shift after meeting with the new environment. The magnitude of the phase shift depends on the ratio between the acoustic impedance of the reflecting medium and that of the medium of propagation of the wave.

In the reflection of sound may occur various specific situations.

For example, in a reflection from a plane surface we have a sense of so-called. virtual sound source located behind the surface. The analogy with the virtual image in the mirror with the reflection of light waves is complete.

This is because the wave propagates spherically and the impact is offset in phase over the same front. The feeling in this moment  is like of a point sound source located behind the barrier:

Other special cases are often found in the acoustics are reflections from planes with a certain profile other than plane surface. Generally we can consider the reflection from convex and concave surfaces.

In the convex we talk about sound leakage.

When we have a straight wave front and a wavelength smaller than the  curvature of the surface, we can observe scattering of the wave under a relatively wide angle.

Since in acoustics of the rooms frequently the focus of the sound waves is undesirable and we often are looking for a larger dispersion, such forms frequently are used in interior design to reduce the correlation of arrival of the sound:

Facioli Hall – Hall of well-known manufacturer of pianos, which uses curved deflectors for spreading the sound, especially in the corners where it shows the opposite trend.

Along with that we often have use of convex surfaces when we need to irradiate a larger area from one

spot sound source, without losing most of the reflected energy:

Conversely, concave surfaces tend to focus the sound energy:

In some cases it may be useful, for example in a situation where we want to use the principle of the satellite dish to focus a remote sounds through a microphone with the corresponding construction:

On the other hand, in the architecture are often used cupolas not only from the perspective of the building construction, but also to the need for focusing and the return of the sound energy from distant points of the room.

In case of a sound source located at the focus point, which is part of the dome, we may have the effect of directing the waves in a given direction as a straight wavefront:

This applies to cupolas with parabolic shape.

The same effect is used in the light reflectors of the headlamps.

For this reason, for example we can distinctly hear the beating of the wings of a bird trapped under a dome or bell tower of a church.

Another phenomenon is the so called “Whispering Gallery”. Still Bach, who has had practical experience in acoustics of churches because of his participation in procedure for adopting the church organs as a representative of the administration, is seen during a visit to a church that there can be observed an interesting effect. If a man stands at one end of the gallery facing the wall and whispers, he will be heard by another, standing on the other side facing the wall, and turned in the other direction:

However standing in the middle might not hear anything from the whispering.

Here we see a similar phenomenon, but in the horizontal direction, where the spherical wave is converted into a flat wavefront and thus we have precise targeting to a single plane of the space.On the other hand, such flat fronts directed towards another reflector, focus the  wave at a specific point. This effect is achieved due to the parabolic shape of the ceiling, which focuses the energy and does not permit it to be dispersed upwards, as usual.

Famous architectural examples as the cathedral St. Paul, basilica “St. Peter” in the Vatican have such galleries.

When there is a need for such a concentration, this effect is useful. So for example in the tiered structure of the scene, as well as in the construction of ceilings in some rooms, especially in the field of  second and third balcony where applicable clever designs to manage the sound energy to reach those distant points sufficiently.

Out of these cases reflecting by concave surfaces is not useful when we are trying to create a homogeneous sound field in a room.

Surfaces which are part of a cylinder, sphere or ellipsoid, are not useful for this homogeneity and should be avoided in the studios and control rooms.

## Retroreflection. CORNER REFLECTION

Retroreflection is on the principle of retro reflective surfaces in nature – such as dew or the retina of some animals, reflecting the light in the dark. This principle is used in the reflective signs on the road and in the reflection elements of the cars. Inside surface appear as filled with tiny pyramids, yielding more than one reflection. In this situation, the wave that is oriented in a certain direction returns to the first direction.

Same with drops of dew. First is created light refraction on the outside of the bubble, and then – a secondary refraction as a result of reflection from the inner side, wherein the first light has penetrated.

As we see, this applies also in technology.

The same situation we have with sound waves.

Due to the angular reflection can be obtained a situation in which the sound wave can be returned back to the source:

As we can see from the graph, similar angular reflections tend reflected signal to follow the direction of the source. Angle reflections are received in acoustics often due to the rectangular shape of most rooms. This is the reason in the presence of perpendicular angles (which should generally be avoided) to be applied sound absorption or dispersion of the sound in places like studios or control rooms.

## Specular and Diffused Reflections

As we said, the angle of incidence equals the angle of reflection. And if we have a flat surface of the reflection, the analogy is like a mirror.

In the presence of a sound wave reflected in a surface, the position of the source and of the listener determines the point of reflection (if the incident wave is at the point P, we are at the point Q).

On rough surfaces we have a diffuse reflection.

When the angle of reflection it is not correlated with the incidence angle, since the surface roughness is causing multiple reflections of different intensity in different directions.

As we see, the very roughness creates a condition to such reflections.

Under similar conditions is formed not a reflective beam, but a spot, which is itself the diffuse reflection.

Why this happens? Because of the equal angle of the incident and the reflected wave to the normal. In a rough surface the normal faces  different directions in different places of the plane:

which leads to different directions of the reflected wave rays.

It is important to bear in mind that the diffuse reflection does not depend as a position from the viewer / listener, but only from the source. We can illustrate it this way:

Here we can see on the one hand, the spot of the diffuse reflection, and on the other – the point of the specular one. In our movement towards the source the point of the reflection will move and the diffuse spot will be permanent.This is because it depends only on the position of the source, and on its angle relative to the reflecting surface, not from the angle of reflection.

So far studied examples such as standing waves, combined filtration, etc. are also examples of the reflection of sound waves, but in a situation of more than one reflection where we have interference between the source and reflection, or between two reflections, or between two sound sources.

### Written byHristo

Filed under: Sound theory