Acoustics - Axial modes behaviour

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As already mentioned, an axial mode consists in an acoustic wave between two surfaces whose wavelength is a multiple of the distance between the two surfaces, where the frequency of the wave in question is called resonance frequency. Now let's take a closer look at what actually happens, referring to the following diagram:

Environmental acoustics - Compression and rarefaction of the particles in a room

Compression and rarefaction of the particles in a room

We have just said that a primary axial mode's wavelength is double the distance between the two surfaces:

λ = 2 d, in other words d = λ/2

The diagram shows us the same wave oscillating continuously between its two opposite conditions. In the first condition (the blue line in the diagram), compression is at its highest on the left-hand side wall and at its lowest on the right wall (where in fact dilation is at its peak). In the second situation (the red dotted line in the diagram), compression is at its highest on the right wall and at its lowest on the left wall (where dilation is at its peak); let's jump back into the bath-tub where we left our hand waving back and forth attempting to get some resonance. The air particles (water particles in our bath-tub), travel from one end to the other at a certain speed. This speed shall be at its peak in the centre of the room (bath-tub), whereas it will be close to zero next to the walls. A more detailed description is given in the following diagram, where the rate of the particles' speed is illustrated (dotted line):

Environmental acoustics - Pressure and speed of the particles in a room

Pressure and speed of the particles in a room

The blue continuous line in the previous diagram illustrates the distribution of sound pressure throughout the room. We can see how next to the walls pressure is at its peak, whereas at the centre of the room pressure is at its lowest. This occurs when the particles on the walls are pressed by the wave and are thus compressed, which essentially means that they are subjected to a certain pressure. Vice versa, the particles at the centre of the room move with the wave and are therefore not subjected to pressure. The areas where pressure is highest are called hot spots, those where pressure is lowest are called cold spots. In the figure we can see that the particles' highest speed (which corresponds to the lowest pressure exerted on them) is present at the centre of the room, in other words at position λ/4. This law is generally applicable so long as the room's dimension is a integer multiple of the wavelength. The following diagram shows the section of a room whose length is four times the wavelength (top diagram). The bottom diagram illustrates the speed-rate and the sound pressure along the room's length:

Environmental acoustics - Characteristics of a non-primary axial mode

Characteristics of a non-primary axial mode

We can see how at a distance λ/4 from the wall, the particles reach their top speed[20 ]. This result shall be useful in a moment, when we will look at the positioning of absorption panels. We can hear the differences between hot and cold spots by generating a resonance frequency inside a room with an oscillator. If we were to enter this room we would indeed be able to hear the differences between the hot and cold spots. If we were to walk from the wall towards the centre of the room, we would gradually hear a clear change in the sound we are perceiving, reaching its peak at a distance of λ/4. This will have meant that we have reached the cold spot, λ being the wavelength of the resonance frequency we have generated.



[20 ] To avoid mix ups, we must point out once again that a particle transporting sound oscillates backwards and forwards in relation to its initial position, transmitting its oscillations to the adjacent particles: it does not travel with the wave along its direction of propagation.








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