Audio Engineering

Microphone Technology 655



L

Figure 22.4 : Simplifi ed illustration of a single diaphragm that is sensitive to a combination of

pressure and pressure gradient.

The center of the porous screen to the right of the diaphragm is separated from the
corresponding point at the center of the diaphragm by an acoustical distance that
amounts to ( d  L ), where d is the diameter of the diaphragm. We need now to calculate
the acoustic pressure at a point just to the right of the center of the porous screen. The
acoustic pressure in the incident wave on the diaphragm is a known quantity, p 1. As
was done in the case of the pressure gradient microphone, we fi rst calculate the rate
of pressure change with distance along the direction of propagation. Next, we fi nd the
component of this change in the direction of interest. Finally, we multiply this component
by the acoustical distance between the points of interest. This last step yields the pressure
change. What is desired of course is the pressure at the second point. This is the pressure
at the initial point plus the change in pressure. Upon lettingp 2 represent the acoustical
pressure at a point immediately to the right of the center of the porous screen, then

ppdL p

r

21 ()cos .θ 1

∂

∂

(22.24)

The driving force that actuates the diaphragm, however, is the pressure difference
betweenp 1 and the pressure in the cavity to the rear of the diaphragm multiplied by
the surface area of one side of the diaphragm. A detailed analysis would show that the
pressure in the cavity, pe , depends on both p 1 and p 2. Recall that for a pressure-sensitive
microphone, the diaphragm driving force is directly proportional to the acoustic pressure;