Sound theory: behaviour of sound

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In this section we'll be taking a look at the way sound behaves when it interacts with obstacles on its path. Generally the nature of these interactions depend as much on the material the obstacle is made of and its dimensions as the sound frequency content does.

The behaviours we'll be looking at mostly relate to waves in general but we'll concentrate on sound waves. These are:

  • Reflection

  • Diffraction

  • Refraction

  • Absorption

1.10.1. Reflection

As our reference, let's look at the figure showing a soundwave hitting a surface and reflecting off it. It's important to be aware that the wave fronts generated by the compressions and dilations are perpendicular to the direction of the propagation of the wave:

Sound theory - Reflection

Reflection

A wave hitting a flat surface with an incidence angle of α (between the normal to the surface and the direction of the wave) is reflected at a reflection angle of α degrees. In the figure we observe an example of a flat surface and then a concave surface in which all the reflected rays converge in the focus point of the curved surface (to know more about focus points you are advised to read any geometry textbook. For our purposes it suffices to say that in a circumference, or sphere in 3D case, 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. However they are used for the construction of directional microphones, as they allow signals (very weak ones too) to be picked up.

Vice versa convex surfaces diffuse sound and are thus greatly used to improve the acoustics of environments.

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



1.10.2. Reflections inside a room

Sound theory - Reflections inside a room

Reflections inside a room

When a sound gets diffused 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 shortest route between the source of the sound and the listener. After the direct signal, arrive the signals that have undergone one reflection only, 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 textbooks). After a further delay come all the signals that have undergone more than one reflection, with an amplitude that is yet inferior to the early reflections. These are called reverb cluster, taking their name from the fact that they are not considered individually but as a single body. The previous figure shows us the distribution of these signals in time, and their amplitudes.



1.10.3. Refraction

This term refers to the phenomenon by which a wave that crosses two media of different densities changes direction as it passes from one to the other. This behaviour is easily explainable if we recall what we said about the speed of sound in media of different densities.

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

Sound theory - Refraction

Refraction

Walls have a greater density than air and therefore wave fronts that begin to penetrate the wall are faster than those that are still outside it. So, as it enters the wall the very same wave front has a faster part (the one already inside the wall) and a slower part (the one still outside the wall). When the whole wave front has fully penetrated the wall, its direction 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, radically modifying the diffusion of sound in the environment.

Sound theory - Open-air refraction

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 figure (top picture).

In the evening we have the opposite situation and the denser layer (cold air) becomes the inferior one. This causes sound to move downwards, as highlighted in previous figure (bottom picture). This has to be taken into careful consideration when organizing an open-air concert [Live sound ] seeing that the long setup process takes place many hours before the concert begins and therefore the atmospheric conditions will inevitably change by the time it starts.



1.10.4. Diffraction

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



1.10.5. Absorption

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

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

Sound theory - Reflection, diffusion, refraction and absorption together

Reflection, diffusion, refraction and absorption together










  • posted on 07-04-2011 13:03
    The top picture is right - but because the wall is stiff, not because it is dense. The pictures of refraction in the open air are right - but note that the sound travels more slowly in the colder, denser air. The bottom picture shows refraction in the wrong direction - as if it was light going through a block of a denser medium.