648 Chapter 22
is propagating along the horizontal axis. The diaphragm may be circular as in a capacitor
or moving coil microphone or rectangular as in a ribbon microphone. The principal axis
of the microphone is directed perpendicular to the plane containing the diaphragm and,
as illustrated, forms an angleθ with the direction of the incident sound. When θ has the
value π /2, both faces of the diaphragm experience identical pressures and the net driving
force on the diaphragm is zero. Now when θ is 0, the sound wave is incident normally on
the diaphragm and the driving force on the left face of the diaphragm will be the pressure
in the sound wave at the left face’s location multiplied by the area of the left face.
The diaphragm material, however, is not porous so sound must follow an extended path
around the diaphragm along which the sound pressure can undergo a change before
reaching the right face. The net driving force on the diaphragm will be the difference in
the pressures on the two faces multiplied by the common diaphragm surface area. The
pressure difference can be calculated by taking the product of the space rate of change of
acoustic pressure, known as the pressure gradient, with the effective acoustical distance
separating the two sides of diaphragm. The least value of this distance is the diaphragm
diameter in the case of a circular diaphragm.
For a ribbon diaphragm the appropriate value would approximate the geometric mean of
the diaphragm’s length and width. Details of a particular microphone housing structure
that provide a baffl e-like mounting will tend to increase the effective separation. If θ is
not zero, the microphone axis is inclined to the direction of the incident sound and the
pressure difference is lowered according to the cosine of the angle.
As a fi rst case, consider that the sound source is quite distant from the microphone
location so that that the incident sound can be described by a plane wave. The
mathematical description of such a wave where the direction of propagation is that of
thex axis is
pxt(,) p em jtkx()ω , (22.7)where pm is the acoustic pressure amplitude, ω is angular frequency 2 π f, k is
propagation constant ω / c 2 π / λ , c is phase velocity, and λ is wavelength.
Under this circumstance, the net driving force acting on the diaphragm in the direction
of increasingx is given by evaluating the following expressions with x set equal to the
coordinate of the diaphragm’s center.