Precision in Sound - page 1

A sound transducer with a flat, flexible diaphragm working
with bending waves
Daniela L. Manger
Manger Products, Industriestrasse 17, D-97638 Mellrichstadt, Germany
Summary:
From the idea to a finally excellent working sound transducer a period of over twenty years was
necessary. Nowadays it is possible to present a wide-band sound transducer working from 100 Hz to 35 kHz. It
follows time-precise without any mechanical energy storage the incoming signal. The special structure of the flat
pliable diaphragm works concentrically only with bending waves. Theoretical equations and measurements will
be presented in comparison to the omnipresent piston loudspeaker. The advantages in perception and hearing
will be mentioned for further research.
INTRODUCTION
In this paper the author will outline the basic theory of the bending-wave sound transducer as
a resistive controlled driver in comparison to the piston loudspeaker. The fundamental de-
scriptions has been made by Rice and Kellogg, comparing the elastic, resistance and mass
controlled units for harmonic motion [1]:
elastic control
.
)(
const
K
F
X txKF
= =⇒ ⋅ =
(1)
resistive control
f
X
fR
F
R
F
X
dt
dx
tu tuRF
1
~
2
)( )(
⇒ = =⇒ = ∧ ⋅ =
π
ω
(2)
mass control
2
2 2
2
2
2
1
~
4
)( )(
f
X
mf
F
m
F
X
dt
xd
ta tamF
⇒ = =⇒ = ∧ ⋅ =
π
ω
(3)
The kinds of energy are for the elastic-controlled motion potential energy, for the resistive-
controlled translation energy and for the mass-controlled kinetic energy. Further research on
mechanics and structure-borne sound about a resistive behaviour let to the realisation of the
resistive-controlled driver [2].
THEORETICAL DESCRIPTIONS
1.
The mass-controlled driver
The theoretical description is known from the literature. The sound pressure is proportional to
the acceleration of the piston, shown in the formula [3]:
)
( ~), ,(
)
(
4
²
), ,(
0
c
r
tA tzrp
c
r
tA
z
a
tzrp
⇒− 
=
ρ
(4)
p(r,z,t)
= sound pressure at position r, z at time t
c
= speed of sound in air
A(t-r/c)
= acceleration at time (t-r/c)
ρ
0
= density of air
a
= radius of circular piston
1 2,3,4
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