16 Jun
2011
16 Jun
'11
10:11 p.m.
Hi there,
in a discussion today someone asked me where those 60 degrees necessary
for the production of phantom images come from and I couldn't deliver a
satisfactory answer. Someone tried to explain to me that it has
something to do with wavelengths or whatever but couldn't explain it in
a way that anyone would understand.
My best guess is that with a larger angle the head gets in the way and
the ears have an easier time telling the signals apart. Also, I guess 60
degrees is a rough estimate and chosen because this leads to a nice
Equilateral triangle.
So, what's the real reason behind those 60 degrees?
Regards,
Philipp
16 Jun
16 Jun
10:21 p.m.
Hello Philipp!
I suppose with 60 degrees you mean the two times 30 degrees, that the
speakers should have. I always thought it had very trigonometrical reasons. So
at your head you have an angle of 120 degrees, which is a wide angle, that
might fit the ears nicely, since they don't look like they would make a 90
degrees angle at your point of the triangle. Something in the back of my mind
tells me phases came in as well. But unfortunately I have nothing more
definite. Someone will though. Fons should, since I think he once explained it
to me with perfect reasoning. So should a few others.
Sorry, I couldn't be more specific.
Warm regards
Julien
--------
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======== FIND MY WEB-PROJECT AT: ========
http://ltsb.sourceforge.net
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======= AND MY PERSONAL PAGES AT: =======
http://www.juliencoder.de
10:41 p.m.
Excerpts from Julien Claassen's message of 2011-06-16 22:21:43 +0200:
Hello Philipp!
I suppose with 60 degrees you mean the two times 30 degrees, that the
speakers should have. I always thought it had very trigonometrical reasons. So
at your head you have an angle of 120 degrees, which is a wide angle, that
might fit the ears nicely, since they don't look like they would make a 90
degrees angle at your point of the triangle. Something in the back of my mind
tells me phases came in as well. But unfortunately I have nothing more
definite. Someone will though. Fons should, since I think he once explained it
to me with perfect reasoning. So should a few others.
Sorry, I couldn't be more specific.
Warm regards
Julien
Thanks for your response Julien,
yes, I mean the two times 30 degrees in front of you.
I hope to get a reasonably scientific answer (if it exists).
Regards,
Philipp
17 Jun
17 Jun
2:45 p.m.
Philipp:
...
I hope to get a reasonably scientific answer (if it
exists).
...
Try something on [1], e.g. [2,3,4].
[1] http://www.sengpielaudio.com/Unterlagen01.htm
[2] http://www.sengpielaudio.com/TheorieGrundlaIntensitaet.pdf
[3] http://www.sengpielaudio.com/TheorieGrundlaAequivalenz.pdf
[4] http://www.sengpielaudio.com/TheorieGrundlaLaufzeit.pdf
Regards,
/Karl Hammar
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+46 173 140 57
16 Jun
16 Jun
10:35 p.m.
On Thu, Jun 16, 2011 at 10:11:25PM +0200, Philipp wrote:
Hi there,
in a discussion today someone asked me where those 60 degrees necessary
for the production of phantom images come from and I couldn't deliver a
satisfactory answer. Someone tried to explain to me that it has
something to do with wavelengths or whatever but couldn't explain it in
a way that anyone would understand.
My best guess is that with a larger angle the head gets in the way and
the ears have an easier time telling the signals apart. Also, I guess 60
degrees is a rough estimate and chosen because this leads to a nice
Equilateral triangle.
So, what's the real reason behind those 60 degrees?
Just what you suggest: it leads to an equilateral triangle and
that *suggests* there is something fundamental about it. But as
far as I know there isn't. Another reason may be that +/- 30
degrees corresponds to the perspective of an average listener
in a concert hall - probably more than say +/- 45 degrees.
OTOH, a recording technique like e.g. Blumlein (two fig-8 mics
at 90 degrees) would suggest a speaker angle of 90 degrees
instead.
A wider angle will make near-center sources less stable. The
number that matters here is the magnitude of the velocity
vector which is cos(1/2 the angle): 0.866 for 60 degrees,
0.707 for 90 degrees, while for a 'real' source it would be 1.
Ciao,
--
FA
10:56 p.m.
Excerpts from Fons Adriaensen's message of 2011-06-16 22:35:10 +0200:
On Thu, Jun 16, 2011 at 10:11:25PM +0200, Philipp
wrote:
Thanks Fons,
this might be the stuff this guy was talking about. Sadly I don't
know how to understand the magnitude of the velocity vector. What does
it represent? Why does the magnitude decrease with the angle?
Best regards,
Philipp
Hi there,
in a discussion today someone asked me where those 60 degrees necessary
for the production of phantom images come from and I couldn't deliver a
satisfactory answer. Someone tried to explain to me that it has
something to do with wavelengths or whatever but couldn't explain it in
a way that anyone would understand.
My best guess is that with a larger angle the head gets in the way and
the ears have an easier time telling the signals apart. Also, I guess 60
degrees is a rough estimate and chosen because this leads to a nice
Equilateral triangle.
So, what's the real reason behind those 60 degrees?
Just what you suggest: it leads to an equilateral triangle and
that *suggests* there is something fundamental about it. But as
far as I know there isn't. Another reason may be that +/- 30
degrees corresponds to the perspective of an average listener
in a concert hall - probably more than say +/- 45 degrees.
OTOH, a recording technique like e.g. Blumlein (two fig-8 mics
at 90 degrees) would suggest a speaker angle of 90 degrees
instead.
A wider angle will make near-center sources less stable. The
number that matters here is the magnitude of the velocity
vector which is cos(1/2 the angle): 0.866 for 60 degrees,
0.707 for 90 degrees, while for a 'real' source it would be 1.
Ciao,
17 Jun
17 Jun
10:58 a.m.
Excerpts from Fons Adriaensen's message of 2011-06-16 22:35:10 +0200:
On Thu, Jun 16, 2011 at 10:11:25PM +0200, Philipp
wrote:
After a little off-list discussion with Gabriel and refreshing my basic
trigonometry a bit I understand your formula, but I still have no idea
what it tells us. The main problem might be that I have no idea how
velocity vectors relate to sound and what the decreasing magnitude tells
us.
Regards,
Philipp
Hi there,
in a discussion today someone asked me where those 60 degrees necessary
for the production of phantom images come from and I couldn't deliver a
satisfactory answer. Someone tried to explain to me that it has
something to do with wavelengths or whatever but couldn't explain it in
a way that anyone would understand.
My best guess is that with a larger angle the head gets in the way and
the ears have an easier time telling the signals apart. Also, I guess 60
degrees is a rough estimate and chosen because this leads to a nice
Equilateral triangle.
So, what's the real reason behind those 60 degrees?
Just what you suggest: it leads to an equilateral triangle and
that *suggests* there is something fundamental about it. But as
far as I know there isn't. Another reason may be that +/- 30
degrees corresponds to the perspective of an average listener
in a concert hall - probably more than say +/- 45 degrees.
OTOH, a recording technique like e.g. Blumlein (two fig-8 mics
at 90 degrees) would suggest a speaker angle of 90 degrees
instead.
A wider angle will make near-center sources less stable. The
number that matters here is the magnitude of the velocity
vector which is cos(1/2 the angle): 0.866 for 60 degrees,
0.707 for 90 degrees, while for a 'real' source it would be 1.
Ciao,
7:48 p.m.
On Fri, Jun 17, 2011 at 10:57:57AM +0200, Philipp Überbacher wrote:
After a little off-list discussion with Gabriel and
refreshing my basic
trigonometry a bit I understand your formula, but I still have no idea
what it tells us. The main problem might be that I have no idea how
velocity vectors relate to sound and what the decreasing magnitude tells
us.
It's not easy to explain without some wave physics and
maths. But I will try :-) Note that I'm simplifying
things a bit, and leaving out a lot of 'ifs' and 'whens'
- some of the things presented below are true only on
some conditions (which you can assume to be satisfied).
Sound consists of variations of air pressure that
propagate as waves. In each point (x,y,z) in space
we have a pressure that is a function of time. Written
as a function, we have P(x,y,z,t), which is called
the _pressure field_.
To generate those pressure variations some air must
move. In each point (x,y,z) the small volume of air
surrounding it has some velocity which is also a
function of time: V(x,y,z,t), _the velocity field_.
While P() is a single value for any given (x,y,z,t),
V() is a vector: it has not only a magnitude but also
a direction. In 3-D space, a vector can be seen as a
combination of 3 independent values, one for each of
the three cartesian coordinates.
One way to look at sound waves is to see them as the
result of the interaction between P and V: they sort
of generate each other, which is what makes the wave
propagate in space.
For a real single sound source the direction of the
vector V(t) is that towards the source, and P(t) and
V(t) in any given point are closely related. They are
of course measured in different units (Pascal, and
meters/second resp.), one is a scalar and the other
a vector, but they are proportional. So given P(t),
we know the magnitude of V(t) - they are the same
signal. An omni mic gives a signal proportional to
P(t), while a figure-of-eight mic gives a signal
proportional to the projection of V(t) on its axis.
For a single source they will produce the same signal
(if you point the bidirection mic to the source).
This is no longer true if we have the same signal
reproduced by two sources, e.g. two stereo speakers
driven by the same signal to generate a virtual
source at the center. The P() will add up, but the
V() add as vectors, so the sum will be shorter than
the sum of the magnitudes, by the cosine factor
mentioned before. So we do not longer have the
fixed relation between P and the magnitude of V.
At low frequencies (where the wavelenght is much
larger than the size of a human head), all the
information we have to determine the direction
of the source is the phase difference between
the signals at the two ears. This is not just a
single value, we can (and do) move our heads and
'explore' this phase difference in function of
those movements.
Now some wave physics and maths will show that
this phase difference depends only on the relative
magnitudes of P() and V() that would exist at the
point halfway between the ears if our head were not
there, and on the direction of our head w.r.t. to
that of the vector V() (and of course on frequency).
What we perceive as the direction of the source is
the direction of V(). But if the magnitudes of P()
and V() don't have the right ratio, the phase
difference will not be as expected by our brain,
and this will make the virtual source less stable
and convincing.
As said this is valid only for low frequencies.
At mid and high frequencies other mechanisms
take over, but these also can be analysed in
terms of the ratio between a scalar sum and
the magnitude of a vector sum, and lead to
similar conclusions.
HTH,
--
FA
20 Jun
20 Jun
11:41 p.m.
On Fri, Jun 17, 2011 at 12:48 PM, Fons Adriaensen <fons(a)linuxaudio.org>wrote;wrote:
For a real single sound source the direction of the
vector V(t) is that towards the source, and P(t) and
V(t) in any given point are closely related. They are
of course measured in different units (Pascal, and
meters/second resp.), one is a scalar and the other
a vector, but they are proportional.
This doesn't matter to the rest of your analysis/description, but I'd offer
a correction to this paragraph.
V(x,t) is proportional to the spatial gradient of P(x,t).
Note that this means pressure and velocity waves are 90 degrees out of sync
with each other.
One clear case this matters is the boundary conditions at walls. The volume
velocity goes to 0 at the wall (Dirichlet), but the pressure has the
requirement that its 1st derivative is 0 (Neumann).
21 Jun
21 Jun
12:33 a.m.
On Mon, Jun 20, 2011 at 04:41:46PM -0500, Charles Henry wrote:
On Fri, Jun 17, 2011 at 12:48 PM, Fons Adriaensen
<fons(a)linuxaudio.org>wrote;wrote:
No, this is wrong. The gradient is 90 degrees out of
phase w.r.t. pressure, and rises by 6 dB/oct w.r.t.
pressure.
The velocity vector is the time integral of the
gradient, and consequently it is in phase with
pressure, and the P/V ratio is independent of
frequency (assuming far field).
Ciao,
--
FA
For a real single sound source the direction of
the
vector V(t) is that towards the source, and P(t) and
V(t) in any given point are closely related. They are
of course measured in different units (Pascal, and
meters/second resp.), one is a scalar and the other
a vector, but they are proportional.
This doesn't matter to the rest of your analysis/description, but I'd offer
a correction to this paragraph.
V(x,t) is proportional to the spatial gradient of P(x,t).
Note that this means pressure and velocity waves are 90 degrees out of sync
with each other.
24 Jun
24 Jun
1:58 p.m.
Excerpts from Fons Adriaensen's message of 2011-06-17 19:48:10 +0200:
On Fri, Jun 17, 2011 at 10:57:57AM +0200, Philipp
Überbacher wrote:
Thanks for your extensive explanation Fons. I slept over it a couple of
days, hoping to understand a little better now.
After a little off-list discussion with Gabriel
and refreshing my basic
trigonometry a bit I understand your formula, but I still have no idea
what it tells us. The main problem might be that I have no idea how
velocity vectors relate to sound and what the decreasing magnitude tells
us.
It's not easy to explain without some wave physics and
maths. But I will try :-) Note that I'm simplifying
things a bit, and leaving out a lot of 'ifs' and 'whens'
- some of the things presented below are true only on
some conditions (which you can assume to be satisfied). Sound consists of variations of air pressure that
propagate as waves. In each point (x,y,z) in space
we have a pressure that is a function of time. Written
as a function, we have P(x,y,z,t), which is called
the _pressure field_.
To generate those pressure variations some air must
move. In each point (x,y,z) the small volume of air
surrounding it has some velocity which is also a
function of time: V(x,y,z,t), _the velocity field_.
While P() is a single value for any given (x,y,z,t),
V() is a vector: it has not only a magnitude but also
a direction. In 3-D space, a vector can be seen as a
combination of 3 independent values, one for each of
the three cartesian coordinates.
One way to look at sound waves is to see them as the
result of the interaction between P and V: they sort
of generate each other, which is what makes the wave
propagate in space.
I found a bit of explanation of wave propagation in one of my books, but
it seems to differ slightly. It basically takes energy and heat into
account and says (simplified) that there are basically two states, one
without motion but increased pressure and heat, one with maximum motion
and little pressure/heat, and everything in between. I guess this
corresponds to P() and V() in your explanation?
For a real single sound source the direction of the
vector V(t) is that towards the source, and P(t) and
V(t) in any given point are closely related.
Towards the source? No idea whether it matters, just wondering.
They are
of course measured in different units (Pascal, and
meters/second resp.), one is a scalar and the other
a vector, but they are proportional.
Proportional or inverse proportional? Again I'm thinking of the model
from the book, with the two states of pressure and velocity. With this
in mind pressure would be large when velocity is small and vice versa.
So given P(t),
we know the magnitude of V(t) - they are the same
signal. An omni mic gives a signal proportional to
P(t), while a figure-of-eight mic gives a signal
proportional to the projection of V(t) on its axis.
For a single source they will produce the same signal
(if you point the bidirection mic to the source).
This is no longer true if we have the same signal
reproduced by two sources, e.g. two stereo speakers
driven by the same signal to generate a virtual
source at the center. The P() will add up, but the
V() add as vectors, so the sum will be shorter than
the sum of the magnitudes, by the cosine factor
mentioned before. So we do not longer have the
fixed relation between P and the magnitude of V.
I understand that the vector sum is different with two speakers,
however, it's somewhat hard to grasp for me that if P() and V() are
generating each other that P() can on the one hand generate proportional
V() and out-of-proportion V().
At low frequencies (where the wavelenght is much
larger than the size of a human head), all the
information we have to determine the direction
of the source is the phase difference between
the signals at the two ears. This is not just a
single value, we can (and do) move our heads and
'explore' this phase difference in function of
those movements.
Now some wave physics and maths will show that
this phase difference depends only on the relative
magnitudes of P() and V() that would exist at the
point halfway between the ears if our head were not
there, and on the direction of our head w.r.t. to
that of the vector V() (and of course on frequency).
What we perceive as the direction of the source is
the direction of V(). But if the magnitudes of P()
and V() don't have the right ratio, the phase
difference will not be as expected by our brain,
and this will make the virtual source less stable
and convincing.
As said this is valid only for low frequencies.
At mid and high frequencies other mechanisms
take over, but these also can be analysed in
terms of the ratio between a scalar sum and
the magnitude of a vector sum, and lead to
similar conclusions.
I guess this sort of analysis or model is used for more complex systems
like ambisonics as well?
HTH,
Yes, thank you very much for your explanation. I've not fully grasped
the "whys", but I understand the idea.
Best regards,
Philipp
3:13 p.m.
On Fri, Jun 24, 2011 at 01:58:47PM +0200, Philipp Überbacher wrote:
I found a bit of explanation of wave propagation in
one of my books, but
it seems to differ slightly. It basically takes energy and heat into
account and says (simplified) that there are basically two states, one
without motion but increased pressure and heat, one with maximum motion
and little pressure/heat, and everything in between. I guess this
corresponds to P() and V() in your explanation?
Can't say without seeing your book. P() and V() certainly
are not 'two states', they are two components of a single
state. You can create any combination of P and V at a
given point.
But for a _single source_ they are related, and you
could map them to voltage and current, with the quotient
being the acoustic impedance (as in Ohm's law).
Again, for the P and V fields generated by a single source
at suffient distance, or a plane wave, P and V are in
phase. Their maxima occur at the same points at any time.
It's very common misconception that the energy in a wave
'alternates' between potential energy (at a P maximum)
and kinetic energy (at a V maximum) as it does for e.g.
a pendulum. Even the Wikipedia article on acoustic waves
gets this wrong. In fact the power is proportional to the
product of P and V (as it is to the product of voltage
and current). If the two were 90 degrees out of phase
the average power would be zero.
I guess this sort of analysis or model is used for
more complex systems
like ambisonics as well?
Yes. In ambisonics the P/V ratio, divided by its expected value for
a plane wave (i.e. the acoustic impedance), is called 'rV'. A good
decoder is designed to generate rV = 1 for low frequencies. It's
done by adding an antiphase signal in a direction opposite to the
intended source. This increases the vector sum of V, and decreases
the sum of P, so they can be made to match again.
Ciao,
--
FA
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12 comments
7 participants
participants (7)
-
Charles Henry -
Fons Adriaensen -
Julien Claassen -
karl＠aspodata.se -
Monty Montgomery -
Philipp -
Philipp Überbacher