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4 - ACOUSTIC COUPLING

The transduction of energy from the sound wave to the movement of the microphone diaphragm is produced by either pressure or pressure-gradient acoustic coupling, or by a combination of both.

4.2 - PRESSURE-GRADIENT ACOUSTIC COUPLING

In the case of a pressure-gradient microphone (i.e. using pressure-gradient acoustic coupling), or more correctly a first order pressure-gradient microphone, the sound wave arrives at both the front and back of the diaphragm. Therefore both the pressure in front and behind the diaphragm vary as a function of the pressure of the sound wave - the force exerted on the diaphragm is generated by the difference in pressure between the front and back of the diaphragm. The term pressure-gradient, which is commonly used to describe this type of acoustic coupling, should really be called pressure- difference, the term ‘gradient’ has a precise meaning in mathematics which must not be confused with the ‘common’ use of this term with respect to microphone acoustic coupling. The surface of the microphone magnetic pole-piece structure will also act as an acoustic obstacle in the path of the sound wave.

As we see with the plan-view of the pole-pieces of a ribbon microphone shown in Figure 7, the sound wave pressure has complete access to both the front and the back of the ribbon surface.



Figure 7 - showing a Pressure-gradient Ribbon Microphone
superimposed on the Sound Wave
It would seem at first sight that the pressure in front of the ribbon should be the same as that at the back, however the effect of placing the acoustic obstacle formed by the ribbon microphone into the path of the sound wave travelling at 340 m/s, creates a difference in the pressure in front and behind the ribbon. The traditional explanation of the pressure-gradient acoustic coupling in a ribbon microphone is to attribute this pressure difference to an apparent path length difference between the sound reaching the front and the back of the ribbon surface – the sound wave is considered as following a longer path length in order to arrive at the back surface of the ribbon as shown in Figure 8.

Figure 8 - Apparent Path Length Difference
We can see the projection of this apparent path length difference onto the wave form at different frequencies in Figure 9.


Figure 9 - Pressure-gradient Coupling at Low, Medium and High Frequencies
(PF is the pressure on the front surface of the ribbon,
PB is the pressure on the back surface)
The theoretical force exerted on the microphone diaphragm is represented in Figure 10.


Figure 10 - Force Exerted on the Microphone Diaphragm
due to Pressure-gradient Coupling
as a function of Wavelength and Path Length Difference (pld)
When the half wavelength exceeds the path length difference, the pressure-gradient acoustic coupling of the ribbon microphone gradually changes to pressure acoustic coupling as the shadow effect becomes more and more pronounced, and this theoretical pressure-gradient response function, shown by dashed lines, is no longer valid.

However plausible this path-length-difference explanation would seem to be, the physics of acoustic coupling as applied to pressure-gradient microphones are in reality far more complex.

First of all, due to the effect of diffraction, in front of the microphone, there is a pressure increase proportional to the wavelength of the sound, as with any reflecting surface placed in the path of the sound wave. Whereas behind the surface created by the ribbon and the pole-pieces the sound is partially masked – a shadow zone is created. The shorter the wavelength, the sharper or more pronounced will be this shadow effect and therefore the more pronounced will be the decrease in pressure behind the ribbon, as shown in Figure 11.



Figure 11 - Soundwave Reflection from the Front Surface of the Microphone
and Pronounced Shadowing Effect behind the Pole-pieces
of a Ribbon Microphone at High Fequencies
With increasing frequency and consequent decreasing wavelength, we therefore have a progressively increasing difference in pressure between the front and the back of the ribbon surface when the sound arrives on-axis. As the wave front passes the pole-pieces, the shadow effect is combined with a secondary emission phenomena clearly defined at higher frequencies, and produced by the corners of the pole-pieces shown in Figure 12.



Figure 12 - Sound Wave Reflections and Shadowing
plus Scattering from the Corners of the Pole-pieces
The corners of the pole-pieces become the source for emission of a secondary spherical wave-front system which will create a complex wave-front pattern behind the ribbon surface - this could be considered to some extent as a justification of path-length-difference theory. The actual strength of the combined wave-fronts as they reach the ribbon will depend very much on the wavelength of the sound wave, and on the symmetry or otherwise of the spherical wave front emission.

As the shadow effect becomes sharper we reach a stage where the pressure behind the ribbon produced by the sound pressure wave is negligible – the pressure within the shadow zone can be considered as purely atmospheric pressure, and the ribbon microphone then is only subject to pressure acoustic coupling.

On the other hand with a decrease in wavelength, both the increase in pressure on front of the pole-pieces and the shadow effect become less and less pronounced as shown in Figure 13.



Figure 13 - Small Shadowing Effect at Low Frequencies
behind the pole-pieces of a ribbon microphone
Whether one considers the force on the diaphragm to be generated by the apparent path length difference or by the different components of diffraction (reflection, shadowing and scattering), the pressure-gradient acoustic coupling function is identical.

Although the ribbon microphone is the classic illustration of pressure-gradient acoustic coupling, moving coil and electrostatic microphones can also be designed with pressure-gradient acoustic coupling, sometimes called phase-shift operation. Basically the sound wave must have access to the back of the diaphragm through some form of opening. Figure 14 shows two possible designs. In both cases the sound wave reaches the back of the diaphragm through a form of acoustical labyrinth, this design technique is normally used to produce a range of different unidirectional microphones - this subject will be considered in more detail in the section on 'Directivity'.


          Figure 14 - A Moving-coil and an Electrostatic
     Pressure-gradient Microphone Capsule