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Date: Fri Jun 13, 2014 3:57 am ((PDT))
I think that it is time to put this argument about the lowest possible atta=
inable sound pressure level to rest.
There seems to be a confusion in terms and perhaps some mixing of apples & =
pomegranates.
Recall that 'dB' is a relative logarithmic measure that is useless without =
some reference level to refer to. Again, dB is always relative!
So when you say 'dBA' or 'dB-anything it is always relative to some absolut=
e reference value.=C2=A0
The commonly used reference sound pressure in air is=C2=A0=C2=A0=3D 20=C2=
=A0=C2=B5Pa=C2=A0(rms) or 0.0002 dynes/cm2,which is usually considered the=
=C2=A0threshold of human hearing.
Our reference for the relative 'dB' values here is an absolute pressure lev=
el of 20 micro Pascals.
Note the words 'usually' and 'threshold of human hearing'. This tells us th=
at 20=C2=A0=C2=B5Pa=C2=A0(rms) has been chosen as the lowest sound pressure=
level that most people can hear, but note that the air does not stop movin=
g at that point and there can be sound pressure levels lower than that, we =
just generally can't hear them with the ears we have. But these low pressur=
e levels do exist and they become negative numbers on the 'dB' scale.
So let's say that there is a insect munching on some leaf at a distance of =
5 feet from us and the sound is measured to be at an absolute sound pressur=
e level of 10 uPa, half of the absolute level of 20 uPa. The calculation fo=
r dB SPL is: =C2=A0dB SPL =3D 20 log(Pmeas/Pref).
In this case, Pmeas =3D 10 uPa, and 20 uPa is always the reference level fo=
r dB SPL.
So let's do the math, starting with the stuff inside the parentheses and wo=
rk our way out:
10/20 =3D 0.5
log 0.5 =3D -0.3010
20 x -0.3010 =3D -6.02 dB SPL
So the sound our insect is making becomes a negative number on the dB SPL s=
cale, since it is relativeto our ear's absolute threshold of perception, bu=
t it still exists as a real sound when measured as an absolute pressure lev=
el. So that is how sound can be lower than '0' when it is measured as dB SP=
L. The corresponding absolute sound pressure level is just less than the ab=
solute reference level. No magic or slight of hand, here.
So yes! If we have sufficiently advanced alien microphone technology, we co=
uld conceivably build a mic with extremely low self noise, perhaps less tha=
n 0 dB SPL (not less than 0 uPA, though! =C2=A0 ;>] ).
Take a look at this:=C2=A0http://www.gras.dk/products/special-microphone/lo=
w-noise-measuring-systems/40hf-1-low-noise-mic-system.html
Be sure to download the complete manual and looks at all of the graphs.
Remarkable!!
Oh, let's now address the thermal noise of the air.
I suspect that in absolute measurement terms, the thermal noise of the air =
is very much lower than the absolute value of 20 uPA. Like, way lower.
Can someone please help out and provide the equations to calculate the 'the=
rmal noise of the air' in absolute terms, i.e., in uPa?
Please give a good description as to what all of this means, too.
I've been looking for this for some time and the search engines are too dum=
b to find me the correct references.
Thanks!
Have a great day,
Greg
From: " [naturerecordists]" <=
ps.com>
To:
Sent: Thursday, June 12, 2014 7:00 PM
Subject: [Nature Recordists] Re: 3032 capsules on PIP
=C2=A0
> Ive been meaning to build a version of the brinibox for quite a long time=
. Id like to "tune" the design if its possible to give at least 10 dB mecha=
nical gain (the gain advantage due to the box boundary layer)
Mike,
The measured on-axis gain on each horn was about 12dB over free air. The
rectilinear conical horn theory is complex, but there are other ways to
describe it.
Note that a rectilinear horn does not have resonances as every incoming
"ray" departs at 180 degrees like a radar reflector. You can't play a
rectilinear horn as you can a tube, narrower cone, or exponential horn like=
a trombone. I used to play one. Note the musicians definition of a gentlema=
n
as someone who can play the trombone but doesn't. :-)
Looking as a rectilinear horn as three reflectors, each with a "boundary
layer" (and I have an explanation for that) the throat point is in effect a=
joint boundary point from three one-third-horn surfaces. In practice the
12dB figure seems about right.
The other way of looking at it, is as two conical horns which each have a
higher acoustic impedance at the throat. This is why I specified sealing th=
e
mic into the thorn throat.
> By placing the mics in the brinibox and taking advantage of the boundary=
effect
> do we reach the ability to record down to the mythical 0 dB SPL?
0dB is impossible. Thermal air noise impinges on both sides of the diaphrag=
m
but the signal only acts on one side, which would give a noise figure of
+3dB over incoming thermal noise. B&K claim the record for an instrumental=
mic of 5dB excess noise. The limit for a practical mic is about 10dB, if
only because some of the incoming sound is reflected away. Even in a vacuum=
,
the atoms in the diaphragm are still moving, but you can do wonders with
creative specs and weighting.
Going back to free air and throat impedances, in free air there is a large=
mismatch between the free air impedance and the diaphragm impedance with
some incoming sound energy being bounced back as above. The same applies to=
the thermal noise of course, but that remains at 3dB above free air. It is=
impractical to evacuate the capsule interior.
Now comes the tricky bit. If you up the signal and thermal sound impedances=
,
they should stay in step, but the signal stays coherent and the thermal
noise stays random, at half the dBs rise. Hence there is a noise benefit by=
using a horn.
This is theory in English, but tests seem to back up the general principle=
of higher gain and lower relative noise.
This is a narrative explanation and I have forgotten how to handle the
required Bessel functions involved. The theory above is only a guide to
trying out variations in practice. I chose the "box" shape as I thought it=
would give a better stereo image and I am happy with the shaking peanuts
test. The rear sensitivity is quite a bit lower which can't be said about
many stereo rigs.
David Brinicombe
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