Audio Engineering

Microphone Technology 651

Ft() jωρ 0 u rt Sd(, ) cosθ. (22.17)

The importance of this result is apparent when Equation (22.17) is compared with
Equation (22.8). With the exception of the identity of the space variable, the two
equations are identical, implying that pressure gradient microphones respond to the
particle velocity in exactly the same fashion whether the incident sound wave is plane,
spherical, or a combination of the two. In contrast, pressure-sensitive microphones
respond to acoustic pressure whether the source is nearby (spherical case) or distant
(plane case). In fact, for a pressure-sensitive microphone the driving force depends only
on the acoustic pressure and is given by the direction independent expression

Ft()p rt S(, ). (22.18)

Another very important aspect of pressure gradient microphones is the proximity effect.
This phenomenon becomes apparent by a rearrangement of Equation (22.16). This
equation is solved for the particle velocity in terms of the pressure and the terms and then
multiplied in both numerator and denominator by the radial distance while making use of
the fact that kω / c  to obtain

urt

jkr

jkr

pr t

c

(,)

(,)

.

1 

ρ 0

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟ (22.19)

The signifi cance of this result is more pronounced when one examines the magnitude of
the particle velocity:

urt

kr

kr

prt

c

(,)

(,)

.

1 ^22

ρ 0

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟⎟ (22.20)

When the radial distance is large or the wavelength is short or of course both of these are
true, then Equation (22.20) reduces to

urt

prt

c

(,)

(,)

 ,

ρ 0