Sound theory: behaviour of sound

Let's take the figure showing a sound-wave meeting a surface and reflecting off it, as our reference example. It's important to be aware that the wave fronts generated by the compressions and dilations are perpendicular to the direction of the diffusion of the wave:

Reflection

A wave meeting a flat surface with an incidence angle of α (between the normal to the surface and the direction of the diffusion of the wave) is reflected at a reflection angle of α degrees. In the figure we can observe an example of a flat surface and a concave surface in which all the reflected rays converge towards the focus point of the curved surface (to know more about focus points you are advised to read any geometry book. For our purposes it suffices to say that in a circumference or sphere, if we consider them in 3D terms, the focus point is the centre).

Concave surfaces are avoided in acoustics as they tend to focus sound in a precise point creating bad sound-distribution. They are however used for the construction of directional microphones, as they allow signals (very weak ones too) to be amplified.

Viceversa convex surfaces diffuse sound and are thus greatly used to improve acoustics in environments.

When a wave reflects on a convex surface, the reflected wave's extension passes through the surfaces focus point.

Reflections within a room

When a sound diffuses in a room (a birds-eye section of which is represented in the previous figure), it reaches the listener in different ways. The first signal that reaches the listener is the strongest one and is the direct one, in other words, the signal that has taken the briefest route between the source of the sound and the listener. After the direct signal, arrive the signals that have received one reflection only, off a wall, and that have therefore a smaller amplitude compared to the direct signal. This is because of the loss of energy that occurs with reflection. We call these signals "Early reflections" ("precocious sound" in some texts). After another delay come all the signals that have undergone more than one reflection, having amplitude that is yet inferior to the early reflections. These are called reverb clusters, whose name indicates the fact that these signals are not considered individually but as a single body. The following figure shows us the distribution of these signals in time, and their amplitudes.

This term refers to the phenomenon by which a wave that intersects two vehicles of different densities changes direction in the course of the passage from one to the other. This behaviour is easily explainable if we bear in mind the things we have said about the speed of sound in vehicles of different densities.

We know that sound travels faster in denser vehicles. Let's consider a wave that meets a wall as shown in the following figure:

Refraction

Walls have a greater density than air and thus wave fronts that begin to penetrate the wall are faster than those that are still outside it. So, at the wall's entrance the very same wave front has a more advanced part (the one towards the inside of the wall) and an anterior part (the one outside the wall). When the whole wave front has fully penetrated the wall, the direction of its diffusion has changed angle. Exiting the wall the same phenomenon occurs but inversely, and the wave returns to its original direction. We will now see how this phenomenon becomes relevant at open-air concerts where conditions change throughout the day, from the morning to the evening, radically modifying the diffusion of sound in the environment.

Open-air Refraction

In the morning the upper layer (cold air) has a greater density compared to the lower layer (warm air) and so sound tends to move upwards as shown in the previous figures.

In the evening the situation is the opposite and the denser layer (cold air) becomes the inferior one. This causes sound to move downwards, as highlighted in the latter two figures. This has to be taken into careful consideration when organizing an open-air concert (live Sound) seeing that the long procedure of preparation and sound-tests takes place many hours before the concert takes place and therefore in atmospheric conditions that will change in the hours to come.

The best way and the most immediate way to describe this phenomenon is to say that it takes place when a sound circumvents an obstacle. This depends greatly upon frequency in that sounds with a great wavelength (and thus a low frequency) easily over-ride obstacles that are smaller than the sound's wave-length. This is one of the reasons why the first frequencies that are attenuated are high ones whilst low ones are diffused over far longer distances.

Absorption can be described as the conversion of acoustic energy into thermic energy by a surface. In other words, when a sound comes into contact with an obstacle, it transfers energy to it which then is dissipated as heat.

Generally speaking these 4 phenomenae are all present when sound meets an obstacle. The following figure illustrates a typical situation:

Reflection, diffusion, refraction and absorption together