Audio Engineering

652 Chapter 22

with the signifi cance that the particle velocity is directly proportional to the acoustic
pressure. However, when r is small or the wavelength is large or a combination is true,
the reduction becomes

urt

r

prt

(,)

(,)

 ,

1

ωρ 0

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟⎟

with the signifi cance that the particle velocity varies inversely with frequency. As
a consequence, when a sound source is in close proximity to a pressure gradient
microphone the lower frequencies of the source produce a larger response than the higher
frequencies. This is the basis for the proximity effect.

One fi nal observation regards the directional characteristics of pressure gradient
microphones. From Equation (22.15), whenθ is in the range π /2  θ  3 π /2, the cosine
ofθ is itself a negative quantity and the polarity of the driving force, as well as the
electrical output signal of the microphone, is reversed. A use will now be made of this
fact in discussing a microphone structure that possesses a variety of several different
directional patterns.

A structure consisting of both a pressure gradient microphone element and a pressure
microphone element makes possible a microphone possessing adjustable directional
characteristics. The elements should individually be small and located close together
with the diaphragms of the two elements located in the same plane. A single signal
based on a linear sum of the signals from the individual elements is generated by the
combination. The root mean square open circuit electrical output of the assembly can
be written as

Eoαβ γ(cos),θ (22.21)

where α is a dimensional constant, β is the fraction of the pressure microphone electrical
signal,γ is the fraction of the pressure gradient microphone electrical signal, and θ is the
angle of incidence of the acoustic signal.

The fractional signals can be formed and summed through the employment of passive
circuitry contained within the microphone housing. The polar response curve of the
microphone for a given choice of coeffi cients is obtained by allowing θ to range
continuously from 0 to 2 π while plotting the curve