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From Power to Source Level
I
Power  10 Gain / 10
p2

Asurf _ at _ 1 _ meter
c
p2 
Power  10 Gain / 10 c
4
 Power  10 Gain / 10 c 


 p2 


4



SL  10 log
 10 log 

12
 up 2 
10
 0 




For Ek60 we had Gain=27 dB Power=300W, ρ=1000kg/m3 c=1485m/s
This gives SL=222.85 dB
For EY500 we had Gain=27.5 dB Power=62.5W, ρ=1000kg/m3 c=1485m/s
This gives SL=216.2 dB
About Source level and Power found on
the net
Source Level (声源级:SL)
A devise which generates acoustic energy is called a
projector. An acoustic projector can take several forms.
Sound transducers convert electrical energy into
mechanical (kinetic) energy which then propagates through
the water as a longitudinal pressure wave. This process is
known as acoustic transduction. The same effect can be
created by using underwater explosions, electrical sparks or
air guns, although these approach is less well controlled.
Here we will concentrate primarily on the acoustic
transduction.
The process of acoustic transduction is a two-way process
as illustrated below:
Electrical Energy <=> Mechanical Energy <=>
Longitudinal Pressure Wave
Transducer
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Hydrophone
A hydrophone is an acoustic listening devise used for
sensing sound underwater. The hydrophone relies on the
reverse process where longitudinal sound waves stress the
surface of the hydrophone sensor (mechanical energy) that
in tern converts the physical displacement into an electrical
signal. This electrical signal can be easily logged and
interpreted by a specialized electrical unit or computer
system. Often the same instrument is used to generate and
receive acoustic energy. In this case the system is termed,
'monostatic'. If a separate projector and hydrophone are
used the system is referred to as 'bistatic'.
Both the process of transduction (hydrophones) and reverse
transduction (transducers) can be achieved by using either
the piezo-electric effect or the principle of
magnetostriction.
The piezo-electric effect: Definition. 'The generation of a
potential difference (voltage) across the opposite faces of
certain non-conducting crystals as a result of the
application of mechanical stress.' The reverse piezo-electric
effect is the opposite to this and is the principle of acoustic
transduction.
About 2/3 of the 32 crystalline classes exhibit the piezoelectric effect. Quartz is a well known example which has
been important in the field of acoustic transduction in the
past. More recently piezo-electric ceramics like lead
zirconate titanate (PZT) are used.
Magnetostriction. This effect utilizes the physical changes
of length of a ferromagnetic material due to the application
of a magnetic field. A simple example is a nickel iron hoop
bound with a magnetizing coil. When an alternating current
energizes the coil a magnetic field is set up which in tern
causes a change in shape of the ferromagnetic material. As
the metal hoop continually changes shape when the
alternating current is applied, a longitudinal pressure wave
is generated in the water. This sort of transduction is
particularly useful for low frequency applications.
Upper Limits To Source Level
You might imagine that the higher the acoustic source level
the more powerful the system, and the longer the detection
range will be. However, there is a distinct upper limit to
this relationship. Generally, sonar range will increase with
the source power until one of two things happen. Firstly, if
the system is used close to the sea surface or bed, or if there
are large amounts of particulate in the water column, back
scattered acoustic reflections (reverberations) may mask
echoes from the intended target. Thus, the sonar range may
actually decrease with further increase in power. Secondly,
if the source level is too high cavitation may occur. This
results in the formation of bubbles on the surface of the
transducer which reduces the efficiency of the transducer
and disrupts the beam pattern of the acoustic pulse.
Calculation of Source Level
Remember that intensity (I) is defined as power (P) per unit
area (A). Also remember that the a quantity expressed on
the decibel scale is given by; N = 10 log(I/Io), where Io is
the standard intensity (= 6.504x10-19W/m2). When
calculating the source level (SL) we consider that sound
from an acoustic source (S) spreads omnidirectionally
(equal in all directions) outwards from the source. We also
take a standard reference distance away from the source of
1m. Thus, our definition of SL on the dB scale becomes:
SL = 10 log(I1 / Io)
SL = 10 log([P1/A1] / Io)
Equation 1
Here I1, P1and A1 are the intensity, power and area
respectively measured one metre away form the source.
The appropriate area here is the surface-area of a sphere
with a radius (R) of 1 metre (A = 4R2 = 4for R=1).
Substituting this into equation 1 we have:
SL = 10 log([P/4] / 6.504x10-19) Equation 2
Where P is the power of the acoustic source. Rearranging
this equation we have;
SL = 10 log(P/ [46.504x10-19])
or equivalently;
SL = 10 log(P) - 10log(46.504x10-19)
Evaluating this we have:
SL = 10 log(P) + 171 (dB re. 1Pa)
Equation 2