As we have already said, the frequencies we have just described are called resonance modes, and are frequencies whose wavelength is a multiple of the distance between two parallel walls. Specifically we call *primary modes*, modes whose wavelengths
[Wavelength
]
are double the distance between the walls.

There are three types of resonance modes:

*Axial*: this type of mode is generated between two parallel surfaces (for example, two walls in a room, or in the space between the floor and the ceiling). The following figure illustrates a primary mode between two parallel walls:Looking at the section of a room, as illustrated in the following figure, we notice the primary axial mode:

We can see how a primary mode's wavelength is double the distance between the two walls. A room has three primary axial modes: one covering its width, one covering its height, and one its length. Clearly there will also be

*secondary modes*present (double the frequency of the corresponding primary mode),*tertiary modes*(triple the frequency) and so on, with amplitudes diminishing as frequency increases. This means that primary modes are the ones that most affect the acoustic response of an environment.*Tangential*: this type of mode is generated when the soundwave reflects on 4 surfaces. The following figure shows an example of a tangential mode:This kind of mode can arise in the following conditions: between the four walls of a room, or between the floor, the ceiling and two walls, or the floor, the ceiling and the two other walls. A tangential mode's amplitude will be smaller than an axial mode's, because it involves four reflections rather than two, which means greater absorption of acoustic energy.

*Oblique*: this mode is generated when sound is reflected off six surfaces in a room. Its amplitude is greatly reduced compared to the other modes. The possible path of an oblique mode is illustrated in the following diagram:To calculate the modes' frequency in a room we'd use the following formula:

**Equation 15.1. Calculation of resonance frequencies of modes**Before you panic, read the next lines, and you'll see that it's not as complicated as it seems. Let's begin by highlighting the quantities present in the equation:

c = speed of the sound in the medium in question (seeing that we are on planet earth we'll take air as the medium through which sound travels. In our case: c = 344 m/s).

l = room length

w = room width

n = room height

n

_{1}, n_{2}, n_{3}= indexes representing the mode.Let's take a look at some examples. Say that we wanted to calculate the frequency of the primary axial mode along the room's length (supposing the width to be l = 10 m). This mode is identified by the following set of three values:

n

_{1}= 1, n_{2}= 0, n_{3}= 0If we substitute these values in the formula we'll have:

**Equation 15.2. Calculation of a primary axial mode**We get a primary axial mode with a frequency value of 17.2 Hz, which is below our audible threshold, and therefore doesn't give us any problems at all.

To identify the resonance modes the following notation is used:

The three primary axial modes are identified by the three triads: 100, 010, 001

The three tangential primary modes are identified by the three triads: 101, 110, 011

The only primary oblique mode is identified by the single triad: 111

Propagation of an axial mode in a room