Introduction to Acoustics

equivalent circuit, as shown in Fig. 5.9b. Similarly, an
important parameter is the quality factor Q, which
measures the ratio between the mechanical energy transmitted
by the transducer and the energy dissipated
(Fig. 5.10). Finally, the equivalent circuit leads to the
measure of the electroacoustic power efficiency k 2 that
corresponds to the ratio of the output acoustic power and
the input electric power.
Hydrophones are usually described with the same
characteristics as transducers but they are only designed
to work in reception. To this goal, hydrophones are
usually connected to a preamplifier with high input
impedance to avoid any loss in the signal reception.
A typical hydrophone exhibits a flat receiving response
on a large bandwidth far away from its resonance
frequency (Fig. 5.11a). As expected, the sensitivity of
a hydrophone is much higher than the sensitivity of
a transducer. Low electronic noise below the ocean
ambient-noise level is also an important characteristic
for hydrophones (Fig. 5.11b). Finally, hydrophones are
typically designed to be omnidirectional (Fig. 5.11c).
5.2.2 Volume Attenuation
Attenuation is characterized by an exponential decay
of the sound field. If A0 is the root-mean-square (rms)
amplitude of the sound field at unit distance from the
source, then the attenuation of the sound field causes the
amplitude to decay with distance along the path, r:
A = A0 exp(−αr) , (5.3)
where the unit of α is Nepers/distance. The attenuation
coefficient can be expressed in decibels per unit distance
by the conversion α ′ = 8.686α. Volume attenuation increases
with frequency and the frequency dependence
of attenuation can be roughly divided into four regimes
as displayed in Fig. 5.12. In region I, leakage out of the
sound channel is believed to be the main cause of attenuation.
The main mechanisms associated with regions II
and III are boric acid and magnesium sulfate chemical
relaxation. Region IV is dominated by the shear and
bulk viscosity associated with fresh water. A summary
of the approximate frequency dependence ( f in kHz) of
attenuation (in units of dB/km) is given by
α ′ (dB/km) =3.3×10 −3 0.11 f 2
+
1 + f 2
+ 43 f 2
4100 + f 2 + 2.98 × 10−4 f 2 ,
(5.4)
a)
C0
R = 1
OP
R0
C = 2OMOP
ù0OF
Underwater Acoustics 5.2 Physical Mechanisms 157
OF
L =
2ù0OPOM
C = OF
ù0
L
C
R
k 2 = 2OPOM
OF 2
b)
Im (Y) (mmhos)
8
20 kHz
7
6
F5
4
3
2
1
0
0
4 kHz
M
ù0
2 4 6 P 8
Re (Y) (mmhos)
Fig. 5.9 (a) Representation of the transducer as an electronic circuit
around the resonant frequency. The resistor R0 corresponds to the
dielectric loss in the transducer and is commonly supposed infinite.
C0 is the transducer capacity, L and C are the mass and rigidity of
the material, respectively. R includes both the mechanic loss and the
energy mechanically transmitted by the transducer. (b) The values of
C0, L, C and R are obtained from the positions of the points F, M and
P in the real–imaginary admittance curve given in the specification
sheet
with the terms sequentially associated with regions I–IV
in Fig. 5.12.
In Fig. 5.6, the losses associated with path 3 only
include volume attenuation and scattering because this
path does not involve boundary interactions. The volume
scattering can be biological in origin or arise from
interaction with internal wave activity in the vicinity
Abs (Y) mmhos)
9
Ym
8
7
6
5
4
3
2
5
Äf
10 15 20
fr
Frequency (kHz)
Fig. 5.10 Frequency dependence of the admittance curve
that allows the calculation of the quality factor Q = fr/∆ f
of the transducer at the resonant frequency fr. Ym is the
maximum of the admittance
Part A 5.2