On Tue, 16 Sep 2003 13:17:53 -0400, "Ethan Winer" ethan at ethanwiner
dot com wrote:

Stewart,

I have done. In my room, you're wrong.

Let's see, your room is 25x18 feet with an 8-9 foot ceiling, and all the
surrounding surfaces are either brick, similarly massive, or 3-layer glass.

Yes, in basic construction.

And you have played low frequency sine waves yet never noticed severe nulls
at 1/4 wavelength (and its odd multiples) away from the room boundaries. You
are either very lucky, very unobservant, or as hel@40th suggests, deaf.

Not luck, just a matter of careful speaker placement and large area
surface treatments (4 off 7x9 foot heavy lined drapes plus 2 large
unglazed paintings and a thick silk rug hung on a 2-inch batten). Also
a thick wool carpet with heavy-duty rubber underlay over most of the
floor area. This surface treatment is mentioned on the webpage you
looked at. A good-sounding room doesn't have to be plastered with your
ugly band-aids!

Of course, with the room unfurnished *and* a single small sound
source, I would obtain quite different results, but that's hardly the
point. If you actually understood basic acoustics, you'd also realise
that the use of sharply angled very large sound sources makes a *huge*
difference to the response smoothness of the room. Luck is not a
factor, but you are clearly inobservant, ignorant, and quite possibly
deaf due to all that time in control rooms (not that this would affect
measurements, so since you claimed that I might be deaf if I couldn't
measure what you did, I guess we'll have to put you down as stoopid
instead). OTOH, you do have a very sharp commercial sense.......
--

Stewart Pinkerton | Music is Art - Audio is Engineering

Stewart,

For a guy who complains about snake oil, it's surprising to see your site
brag about oxygen free copper and other such audiophile nonsense.

If you actually understood basic acoustics ... A good-sounding room
doesn't have to be plastered with your ugly band-aids! ... you are clearly
inobservant, ignorant, and quite possibly deaf ... we'll have to put you
down as stoopid

Why are you so nasty? I haven't been nasty to you. Didn't your mother teach
you any manners?

7x9 foot heavy lined drapes plus 2 large unglazed paintings and a thick
silk rug hung on a 2-inch batten). Also a thick wool carpet with heavy-duty
rubber underlay

None of those things do squat for low frequencies. I'm really surprised you
don't know that.

--Ethan

Randy,

\int\int H(x,y,z,rho,phi,w) He(rho,phi,w) d rho d phi.

You don't need all that - just play a friggin' 100 Hz tone and walk toward
and away from the rear wall! The answer will be immediately obvious.

--Ethan

On Wed, 17 Sep 2003 11:10:02 -0400, "Ethan Winer" ethan at ethanwiner
dot com wrote:

For a guy who complains about snake oil, it's surprising to see your site
brag about oxygen free copper and other such audiophile nonsense.

I see that you are now reduced to the classic 'lies and distortions'
approach, which is pretty braindead since the page is there for all to
see. I do not 'brag' about anything, since I note that the OFHCC
silver-plated Teflon-coated wire is in fact just standard 10 cents a
foot MIL-spec hookup wire!

If you actually understood basic acoustics ... A good-sounding room
doesn't have to be plastered with your ugly band-aids! ... you are clearly
inobservant, ignorant, and quite possibly deaf ... we'll have to put you
down as stoopid

Why are you so nasty? I haven't been nasty to you. Didn't your mother teach
you any manners?

Indeed she did - she especially warned me about cheats and con
artists...................

7x9 foot heavy lined drapes plus 2 large unglazed paintings and a thick
silk rug hung on a 2-inch batten). Also a thick wool carpet with heavy-duty
rubber underlay

None of those things do squat for low frequencies. I'm really surprised you
don't know that.

Sure they do, especially the heavy drapes - I'm not at all surprised
that you don't know that.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Wed, 17 Sep 2003 11:13:37 -0400, "Ethan Winer" ethan at ethanwiner
dot com wrote:

Randy,

\int\int H(x,y,z,rho,phi,w) He(rho,phi,w) d rho d phi.

You don't need all that - just play a friggin' 100 Hz tone and walk toward
and away from the rear wall! The answer will be immediately obvious.

As expected, all sales blarney and no science.................
--

Stewart Pinkerton | Music is Art - Audio is Engineering

Ethan Winer wrote:

Randy,

\int\int H(x,y,z,rho,phi,w) He(rho,phi,w) d rho d phi.

You don't need all that - just play a friggin' 100 Hz tone and walk toward
and away from the rear wall! The answer will be immediately obvious.

--Ethan

Since I don't have a calibrated dB SPL meter in my head, and since
a dB SPL meter doesn't have pinnae and HRTFs, I was attempting to
propose a method to accurately measure what your ears would hear.
What you propose will definitely not accomplish this.
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

On Fri, 19 Sep 2003 00:07:58 GMT, Randy Yates wrote:

Ethan Winer wrote:

Randy,

\int\int H(x,y,z,rho,phi,w) He(rho,phi,w) d rho d phi.

You don't need all that - just play a friggin' 100 Hz tone and walk toward
and away from the rear wall! The answer will be immediately obvious.

--Ethan

Since I don't have a calibrated dB SPL meter in my head, and since
a dB SPL meter doesn't have pinnae and HRTFs, I was attempting to
propose a method to accurately measure what your ears would hear.
What you propose will definitely not accomplish this.

Ah yes, but it *does* drive fear into the heart of the prospective
customer, which is what counts........ :-)

Use two ear-spaced mics, and/or a large sound source, and you don't
get this problem.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

And even if it wasn't immediately obvious doesn't mean it doesn't happen - given
the binaural receiver (the head) is the acoustical equivalent of a dual
diversity FM receiver - designed not to notice dead spots, especially at low
frequencies where the ears are not so direction-sensitive.

On Wed, 17 Sep 2003 11:13:37 -0400, "Ethan Winer" ethan at ethanwiner dot com
wrote:

Randy,

\int\int H(x,y,z,rho,phi,w) He(rho,phi,w) d rho d phi.

You don't need all that - just play a friggin' 100 Hz tone and walk toward
and away from the rear wall! The answer will be immediately obvious.

--Ethan


Regards,
Tony (remove "_" from email address to reply)

Randy,

I was attempting to propose a method to accurately measure what your ears
would hear. What you propose will definitely not accomplish this.

An omnidirectional microphone will capture the exact same pressure changes
as your ears. And there's no need for the meter to be calibrated because
you're looking for the *relative* change in level.

The point I've been making all along is you don't really need meters or
mikes or test gear. Even if walking toward and away from a wall doesn't give
an exact dB measurement of null depth, at least it proves the existence of
deep nulls. Dick and his followers continue to dispute that such severe
nulls even occur at all. And of course you can't begin to solve a problem
until you first understand that it exists!

Once you play the tones and realize there are in fact deep nulls in your
room, *then* you can do a more elaborate test as I explained in the other
thread. Again, nothing needs to be calibrated because all levels are
relative. You find a deep null, measure and note the level, then move the
mike and measure again.

This is not rocket science! :-)

--Ethan

In article ,
Ethan Winer ethan at ethanwiner dot com wrote:
Randy,

I was attempting to propose a method to accurately measure what your ears
would hear. What you propose will definitely not accomplish this.

An omnidirectional microphone will capture the exact same pressure changes
as your ears.

Really? That's an EXTRAORDINARY claim, Mr. Winer. So you are
disputing about 80 years of auditory research? You are disputing
the existance of HRTF? You're disputing the existance of pinnae
transformations?

Where is the evidence supporting your claim?

The point I've been making all along is you don't really need meters or
mikes or test gear.

But you have made SPECIFIC numeric claims, in figures such as Hz
and dB.

Even if walking toward and away from a wall doesn't give
an exact dB measurement of null depth, at least it proves the existence of
deep nulls.

You have claimed "exact" measurements, no you say they are not
necessary?

--
| Dick Pierce |
| Professional Audio Development |
| 1-781/826-4953 Voice and FAX |
| |

Tony,

given the binaural receiver (the head) is the acoustical equivalent of a
dual diversity FM receiver

Good point. The nulls may not be quite as audibly damaging as they measure.
But I assure you they are *very* audible.

--Ethan

Ethan Winer wrote:

Randy,

I was attempting to propose a method to accurately measure what your ears
would hear. What you propose will definitely not accomplish this.

An omnidirectional microphone will capture the exact same pressure changes
as your ears.

Er, no, it won't Ethan. Go check out some of the JAES articles on pinnae
responses and head-related transfer functions circa the early 80's.

And there's no need for the meter to be calibrated because
you're looking for the *relative* change in level.

Of course relative levels don't need calibration. However, if you're
looking at frequency response, then the response needs to be calibrated.
And neither of these is what I intended: that we can discern precisely X
dB with our ears/brain.

The point I've been making all along is you don't really need meters or
mikes or test gear. Even if walking toward and away from a wall doesn't give
an exact dB measurement of null depth, at least it proves the existence of
deep nulls.

Proves? How so? How does one define "deep null?" And how does one establish
the objective correctness of the asserted level differences? I disagree
completely with you here.

Dick and his followers continue to dispute that such severe
nulls even occur at all.

Dick (I believe - this is from memory) disputed that the level
was as deep as you said it was. As the one making the assertion,
I believe the onus is on you to provide objective, verifiable
evidence for your claims if you want certain folks (such as
Dick and myself) to believe your claims.

And of course you can't begin to solve a problem
until you first understand that it exists!

And "understanding it exists" means not relying on subjective
impression but rather verifying objectively.

[...]
This is not rocket science! :-)

Frankly, Ethan, you have no idea what you're talking about. The
pressure field in a room is a HIGHLY complex phenomenom that
requires some very sophisticated engineering and analysis
principles to understand completely. I think you need to
stick with sales.
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

"Ethan Winer" ethan at ethanwiner dot com wrote in message

Stewart,

Because I don't agree with your claims that support your sales
campaign?

No, because if you had played sine waves and walked around *slowly and
carefully* you'd know I am right!

At this point, it seems advisable to stop teaching the hog to sing

That pretty well sums up my hope to ever get through to you too.

For a group of guys that claim to enjoy technical issues, this sure
has been one-sided. I spent two hours looking through the references
you linked, I did some further searching of my own, and spent half an
hour discussing this with my DSP expert friend. You guys, on the
other hand, can't be bothered to play a 100 Hz tone for 2 minutes
while you walk toward and away from the walls.

At this point I have to assume you did try sine waves, realized I'm
right, and are now saying you're "tired of this" as a way to save
face. Yes?

Probably not.

I have to admit that I'd have done the experiment in a heartbeat if I could
just remember where my $#@! RS SPL meter is located. The embarrassing
revelation is that I don't know where it is at the moment. This relates to
the fact that I own about 8 pairs of diagonal side-cutting pliers but never
seem to be able to find one when I need it!

My main stereo is currently disconnected from any computers or signal
generators, but how long would it take me to generate some wav files and
burn an audio CD with a 100 Hz sine wave on it? I can find my blank CDs
pretty easily given that I have a few hundred of them kicking about the
house (but in at least 4 different locations). ;-)

Meanwhile, I'd like to shed some light on the potentially fallacious
thinking that you've been facing, Ethan. We've had plenty of recitals of the
fact that 100 Hz waves are about 9 feet long and therefore it is claimed
that any nulls along standing waves @100 Hz would have to be like 9 feet
apart or something like that. Nit pickers should notice that 9 feet is just
an order-of-magnitude number.

The statement that is raising people's hackles is that Ethan says that nulls
due to 100 Hz standing waves in a room can be inches apart.

IME, they can.

So what about the 9 foot wavelength of a 100 Hz wave? True enough for a wave
propagating along a 1-dimensional line. The big problem for your critics
Ethan is that we're talking standing waves propagating in a 3-dimensional
room, not waves propagating along a 1 dimensional line.

The SPL at any point in a room is the vector sum of the pressure due to
waves propagating in a large number of directions. Pressure from a
floor-to-ceiling bounce can cancel pressure from a wall-to-wall bounce at
one point, and a wall-to-wall bounce operating in a N-S direction and cancel
another wall-to-wall bounce operating in the E-W direction near by. Two
nulls, but a lot less than 9 feet apart. Perhaps only inches separate them.


The SPL meter's relatively small omni mic isn't directional at 100 Hz, so
all it can do is report the vector sum of the pressures summing at a point
approximately at the center of its diaphragm. Any information about the
actual directions the waves creating the pressures are propagating in, is
summed out.

Bottom line is that standing waves in a room are very complex, and as one of
your critics actually said (paraphrasing slightly): It's a mistake to think
that one can characterize a room in a couple of minutes.

Therefore, it's possible to find peaks and nulls that are a lot less than 9
feet apart in a room being excited by a 100 Hz sine wave. Been there done
that and would do it again in a heartbeat if I could just remember where
that $##! RS SPL meter is.

One sees another real-world example of this when waves on a lake concentrate
in odd-shaped reflective areas like one finds around boat docks and piers.
The long waves on the lake end up as a mass of small chop when reflections
from various angles combine in a small area. It's the same old vector sum
rule, this time mostly in just two dimensions.

Arny,

I'd have done the experiment in a heartbeat if I could just remember where
my $#@! RS SPL meter is located.

You really don't need a meter. Once you hone in on the deepest part of a
null by ear, just turn your head a few inches and the level will come WAY
up. A meter will tell you if it's 15 dB or 25 dB, but you ears will tell you
it's a big change regardless of the exact numbers.

I own about 8 pairs of diagonal side-cutting pliers but never seem to be
able to find one when I need it!

I can't tell you how many times I've driven all the way to Home Depot to buy
something or other, only to get back home and find I already had one!

The statement that is raising people's hackles is that Ethan says that
nulls due to 100 Hz standing waves in a room can be inches apart.

The mechanism is much simpler than what you described. Yes, a null near a
wall can be near a null from the floor or ceiling. But that's not needed to
have a big change in level across a small distance. The real issue is that
the null is extremely deep at a given location due to near-complete phase
cancellation. As soon as you move the smallest amount the cancellation is
slightly less, but that's enough to make the level come up a lot. There's
probably a term for this behavior - it's not Q - but I'm not sure what it
is. Ah, I know a good analogy:

You and Dick and some of the others here are probably old enough to have
measured distortion with a nulling filter device like the old
Hewlett-Packard analyzers. You send a sine wave having very low distortion
into the device under test, and feed that device into the distortion
anayzer. Then you set the analyzer's notch filter to completely cancel 1
KHz. Whatever remains is distortion and noise. The key point is the filter
frequency knob is VERY touchy. It's not that the filter has a Q of 400, it's
just that the null point for maximum cancellation is very precise.

Bottom line is that standing waves in a room are very complex

Yes, absolutely true, and that surely makes it difficult to predict the
response for a given location. The good news is bass traps really help this
problem a lot. :-)

The nulls I've been talking about exist at 1/4 wavelength from every
boundary. The one I measured in my room was 1/4 wavelength from the wall AND
ALSO 1/4 wavelength from the floor. That's where I found the deepest null in
that part of the room. At that place the phase and level of the reflections
were exactly equal and opposite to the main source. As soon as I moved the
mike a few inches the cancellation became much less severe.

--Ethan

Dick -- Bass traps have been a standard acoustic treatment tool in the arsenal
of studio designers at least since the days of Westlake and Tom Hidley in the
70s. The home studio that I had built in my residence in 1979 (designed by
Jeff Cooper) is heavily trapped. There is a good 30 years of art in this area.

Re "deconvolution": As another poster pointed out, exact deconvolution
requires the transfer function of the filter being deconvolved to be minimum
phase. Neely and Allen showed through computer simulations that the source to
receiver room impulse response is generally nonminimum phase. (S. Neely and J.
Allen, "Invertability of a Room Impulse Response," J. Acoust. Soc. Am., vol.
66, pp. 165-169 (1979).) Therefore, in most cases a stable deconvolution
filter does not exist. Your rhetoric regarding deconvolution is largely
handwaving and represents a gross oversimplification of the state of the art
in DSP room correction.

(See http://www.realspace.com/SigTech/aes_90sf.html. for an informed
discussion of the issues.)

I believe that somewhere along the line, you and Mr Pinkerton have confused
the eigenvalues (poles) of the source to receiver room transfer function with
that function's zeros. Zeros do indeed enable very deep and very localized
nulls to occur.

Finally, I must say that I am appalled by yours and Mr Pinkerton's lack of
civility in this thread and applaud Mr. Winer's resisting descending to that
level.

Bob Orban






In article , says...


In article ,
Ethan Winer ethan at ethanwiner dot com wrote:
Who said anything about only one absorber or their being small? The most
popular panels we sell are 2x4 feet and we typically recommend eight for a
normal home-sized room. Friday I supervised installing a set of our traps in
the home studio of a famous record producer. The room is about 13x20 feet
with a vaulted ceiling, and we used ten panels. I'll add that the producer's
engineer was thrilled with the improvement these ten traps made, and before
we left he was emailing a friend at a big-name studio about how cool our
stuff is. I'm not saying this to brag! Just to make the point that THIS is
how real-world acoustics problems are solved.

So you are passing off paraphrased testimonials with no
quantified results from unnamed people who as some "proof?"

Please, why not SHOW us what happened to the 1/3 octave RT60
time as a result of your fabuluous treatments?

Your "walk around the room" measurements show the level of
amateurish stunts you call "measurements."


--
| Dick Pierce |
| Professional Audio Development |
| 1-781/826-4953 Voice and FAX |
| |

"Robert Orban" wrote in message
...
Re "deconvolution": As another poster pointed out, exact
deconvolution
requires the transfer function of the filter being deconvolved
to be minimum
phase. Neely and Allen showed through computer simulations that
the source to
receiver room impulse response is generally nonminimum phase.
(S. Neely and J.
Allen, "Invertability of a Room Impulse Response," J. Acoust.
Soc. Am., vol.
66, pp. 165-169 (1979).) Therefore, in most cases a stable
deconvolution
filter does not exist. Your rhetoric regarding deconvolution is
largely
handwaving and represents a gross oversimplification of the
state of the art
in DSP room correction.

Since you refer to SOA you should cite something more recent than
25 year old research. Non-minimum phase is NOT an issue with
modern techniques.

The "gross oversimplifications" were made for the non-expert
audience of this newsgroup.

I'll let the others debate the snake oil of the bass trap.

In article ,
says...


"Robert Orban" wrote in message
...
Re "deconvolution": As another poster pointed out, exact
deconvolution
requires the transfer function of the filter being deconvolved
to be minimum
phase. Neely and Allen showed through computer simulations
that
the source to
receiver room impulse response is generally nonminimum phase.
(S. Neely and J.
Allen, "Invertability of a Room Impulse Response," J. Acoust.
Soc. Am., vol.
66, pp. 165-169 (1979).) Therefore, in most cases a stable
deconvolution
filter does not exist. Your rhetoric regarding deconvolution is
largely
handwaving and represents a gross oversimplification of the
state of the art
in DSP room correction.

Since you refer to SOA you should cite something more recent
than
25 year old research. Non-minimum phase is NOT an issue with
modern techniques.

My point is that naive deconvolution seems like the theoretically
perfect solution to the problem until one looks at the details, in
which the devil always resides. Please note that I also supplied one
other reference (from 1992) that describes in some detail how one
company with a commercial product (SigTech) dealt with the
problem of nonminimum phase. I am aware of a number of other
techniques, which vary mainly in the way the system identification
is performed, how the resulting complex transfer function is
factored (into minimum-phase and excess phase elements, and
often additionally into frequency bands to which different classes
of treatment are applied), how the measured transfer function is
smoothed prior to equalization, and whether the z-plane equalizing
filter is an all-zero filter or a filter with both poles and zeros.

It is clear that this class of product is useful in some circumstances.
However, the fact that this class of product (DSP-based
loudpseaker/room equalization) has been commerically available for
a good 20 years now without its being found in every good-quality
audio system (or even in more than a tiny minority of them)
indicates to me that it is hardly a pancea.

AFAIK, _all_ of these well-refined techniques take into account the
fact that trying to equalize sharp local minima (something that
happens with naive deconvolution) makes the sound worse
globally, precisely because the minima are so localized. This has
been appreciated ever since Boner's pioneering work with cut-only
analog equalization of the loudpseaker/room magnitude response,
not to mention the original Altec "Acousta-Voice" system, which
used cut-only third-octave analog filter banks.

Finally, regarding the debate about the existence (or lack of same)
of 15 dB nulls at 70 Hz, I refer you to Fig. 6 of:

http://www.genelec.com/pdf/aes114th.pdf

which demonstrates a 15 dB dip at 95 Hz. Not 70 Hz, but close
enough.

This paper also has 42 useful references.

In article ,
Robert Orban wrote:
Finally, regarding the debate about the existence (or lack of same)
of 15 dB nulls at 70 Hz, I refer you to Fig. 6 of:

http://www.genelec.com/pdf/aes114th.pdf

Robert, if you would go back and read the claim, it was not the
EXISTANCE of a 15 dB deep null, ratherm the claim was made that
the sound pressure could change, as I recall the original claim,
by 35 dB over the space of 1 inch at 70 Hz. The refutation was
NOT that deep nulls couldn't exist, but that such an enormous
delta over sucha small distance with such a large wavelength was
difficult to take at all seriously, considering that 1"
corresponds to less that 2 degrees of phase rotation.

That further degenerated into bizzare claims tantamount that a
small "bass trap" had a broadband absorbtion coeeficient well in
excess of 1.

No one was disputing such nulls can exist, rather the rather
extraordinary claims made by a person who has freely admitted
they have nevr measured the sound field and energy distribution
in a room properly at all, yet that same person was making
claims that REQUIRED careful and detailed measurements precisely
this sort.

--
| Dick Pierce |
| Professional Audio Development |
| 1-781/826-4953 Voice and FAX |
| |

In article , says
....


In article ,
Robert Orban wrote:
Finally, regarding the debate about the existence (or lack of same)
of 15 dB nulls at 70 Hz, I refer you to Fig. 6 of:

http://www.genelec.com/pdf/aes114th.pdf

Robert, if you would go back and read the claim, it was not the
EXISTANCE of a 15 dB deep null, ratherm the claim was made that
the sound pressure could change, as I recall the original claim,
by 35 dB over the space of 1 inch at 70 Hz. The refutation was
NOT that deep nulls couldn't exist, but that such an enormous
delta over sucha small distance with such a large wavelength was
difficult to take at all seriously, considering that 1"
corresponds to less that 2 degrees of phase rotation.

That further degenerated into bizzare claims tantamount that a
small "bass trap" had a broadband absorbtion coeeficient well in
excess of 1.

No one was disputing such nulls can exist, rather the rather
extraordinary claims made by a person who has freely admitted
they have nevr measured the sound field and energy distribution
in a room properly at all, yet that same person was making
claims that REQUIRED careful and detailed measurements precisely
this sort.

I did a calculation to determine how deep a null would have to be in order
to have the SPL change by 35 dB over the space of 4"(a number mentioned
repeatedly in the thread) at 70 Hz. Here it is. (If there is an error, please let
me know.)

This requires a monospaced font (like Courier) to display properly:

At 70 Hz, the acoustic phase shift is:

0.032435*radian
_________________
inch

Because air is linear at reasonable SPLs, superposition holds.
Thus, we model a null as two sources of identical frequency but unequal
amplitude
with a phase difference of pi radians at the null. This is consistent with the
idea that
a null represents the zeros of the transmission transfer function, because
zeros are usually created by summation.

To normalize the calculation, assume that the sum of the magnitudes of the
two sources = 1

a1 + a2 = 1

We wish to solve for the null depth, d, required for the magnitude, m, to
change by deltadB.

We define

deltadB/20
del = 10

We define the angle (in radians) by which we move away from the null as
dr.

Then the complex value at this displaced location is:

a1 + a2*(COS(dr) + j*SIN(dr))

And the square of the magnitude at the displaced location is:

2 2
2*a1*a2*COS(dr) + a1 + a2

To facilitate solving the equations, we use the square of del in our
equations.

2 2
2*a1*a2*COS(dr) + a1 + a2 = dispSquare

dispSquare
____________ = delSquare
2
d

We have three equations in three unknowns (a1, a2, d):

a1 + a2 = 1

a1 - a2 = d

2 2
2*a1*a2*COS(dr) + a1 + a2
_____________________________ = delSquare
2
d

The solution is:

SQRT(COS(dr) + 1) 1
a1 = ________________________________ + ___
2 SQRT(COS(dr) + 2*delSquare - 1) 2

1 SQRT(COS(dr) + 1)
a2 = ___ - ________________________________
2 2*SQRT(COS(dr) + 2*delSquare - 1)

SQRT(COS(dr) + 1)
d = ______________________________
SQRT(COS(dr) + 2*delSquare - 1)

Substituting real values for 4 inch displacement, we have:

dr := pi - 0.032435*4

35/20 2
delSquare := (10 )

a1 = 0.5005764712; a2 = 0.4994235287; d = 0.001152942508

RequiredNulldB = 20*LOG10(0.001152942508)

RequiredNulldB = -58.76384696 dB

Magnitude_4inches_displaced = - 23.76384696 dB

Giving us the 35 dB difference, as required.

Robert Orban wrote in message ...

I did a calculation to determine how deep a null would have to be in order
to have the SPL change by 35 dB over the space of 4"(a number mentioned
repeatedly in the thread) at 70 Hz. Here it is. (If there is an error, please let
me know.)

Thanks Robert,

Finally ! Someone took the trouble to do the math to prove that
Ethan's basic argument - that very deep nulls can occur at bass
frequencies that are VERY localised to within a few inches, despite
the long wavelengths of the frequency involved, is true. (I notice the
argument suddenly died at this point)

It's such an empirically easily observable and provable phenomenen
that I can't believe that Richard and Stewart argued against it so
long and so vehmenantly. (Not to mention all the personal attacks and
irrelevant handwaving)

Through the whole thread I had a mental impression of both of them
putting their fingers in their ears and humming real loud

Reading through the entire thread before replying was kind of like
watching a movie where people are sitting at a table eating dinner and
the viewer can see a bomb ticking under the table and you're yelling
at the TV "look under the table damn it!"...

Although I couldn't describe the maths as you did, I already had a
mental picture of the relationship of the cancellation and how with a
sufficiently deep notch (due to very high reflectivity from some
boundry, such as a concrete floor) you could get a large change in
summed response over a relatively small physical displacement, despite
the long wavelengths.

Most of the rooms I've heard speakers in have suffered from at least
one deep null in the midbass at a certain location, typically in the
60-100Hz range, that I don't think I've ever seen an untreated room
yet that *doesn't* have at least one sharp null somewhere.

For example my current room, which has a well carpeted, but solid
concrete floor and walls on two sides that have brick on the outside,
has a *very* deep, *very* narrow notch around 75Hz which is evident in
certain locations in the room, primarily at points along the
centerline of the room, and primarily at lower alititudes. (Sitting or
ducking)

Ducking down in the right place you can find a point of *total*
cancellation, so the reflectivity of the walls or floor contributing
the cancelling waves must be pretty damn close to 100%. (Not
surprising with poured concrete and bricks)

When I say total cancellation, you can't hear a thing if a pure tone
is playing even at moderately loud levels and yet at the same time you
can *feel* the presense of the tone on your body as a vibration, since
the rest of your body is not at the critical point of cancellation.
Quite an unusual sensation to feel a low frequency and not hear it :-)

Move 4 inches to the left or right (a figure bandied about in the
discussion) and the level comes up from not audible to moderately
loud, easily a change of 15dB.

I'm sure as Ethan reads this he'll be thinking "Yep, this is the kind
of thing I see all the time..."

Sometimes I wish people would just put away their formulas and
theories and *try* things, like Ethan's simple enough suggestion to
walk around a room with a sinewave playing, rather than setting out to
disprove the point from the outset on a theoretical basis.

Ethan's suggestion is something so mindbogglingly simple and obvious,
that I've already done it dozens of times in a number of rooms in the
past...

Regards,
Simon

Robert Orban wrote in message ...

I did a calculation to determine how deep a null would have to be in order
to have the SPL change by 35 dB over the space of 4"(a number mentioned
repeatedly in the thread) at 70 Hz. Here it is. (If there is an error, please let
me know.)

Thanks Robert,

Finally ! Someone took the trouble to do the math to prove that
Ethan's basic argument - that very deep nulls can occur at bass
frequencies that are VERY localised to within a few inches, despite
the long wavelengths of the frequency involved, is true. (I notice the
argument suddenly died at this point)

It's such an empirically easily observable and provable phenomenen
that I can't believe that Richard and Stewart argued against it so
long and so vehmenantly. (Not to mention all the personal attacks and
irrelevant handwaving)

Through the whole thread I had a mental impression of both of them
putting their fingers in their ears and humming real loud

Reading through the entire thread before replying was kind of like
watching a movie where people are sitting at a table eating dinner and
the viewer can see a bomb ticking under the table and you're yelling
at the TV "look under the table damn it!"...

Although I couldn't describe the maths as you did, I already had a
mental picture of the relationship of the cancellation and how with a
sufficiently deep notch (due to very high reflectivity from some
boundry, such as a concrete floor) you could get a large change in
summed response over a relatively small physical displacement, despite
the long wavelengths.

Most of the rooms I've heard speakers in have suffered from at least
one deep null in the midbass at a certain location, typically in the
60-100Hz range, that I don't think I've ever seen an untreated room
yet that *doesn't* have at least one sharp null somewhere.

For example my current room, which has a well carpeted, but solid
concrete floor and walls on two sides that have brick on the outside,
has a *very* deep, *very* narrow notch around 75Hz which is evident in
certain locations in the room, primarily at points along the
centerline of the room, and primarily at lower alititudes. (Sitting or
ducking)

Ducking down in the right place you can find a point of *total*
cancellation, so the reflectivity of the walls or floor contributing
the cancelling waves must be pretty damn close to 100%. (Not
surprising with poured concrete and bricks)

When I say total cancellation, you can't hear a thing if a pure tone
is playing even at moderately loud levels and yet at the same time you
can *feel* the presense of the tone on your body as a vibration, since
the rest of your body is not at the critical point of cancellation.
Quite an unusual sensation to feel a low frequency and not hear it :-)

Move 4 inches to the left or right (a figure bandied about in the
discussion) and the level comes up from not audible to moderately
loud, easily a change of 15dB.

I'm sure as Ethan reads this he'll be thinking "Yep, this is the kind
of thing I see all the time..."

Sometimes I wish people would just put away their formulas and
theories and *try* things, like Ethan's simple enough suggestion to
walk around a room with a sinewave playing, rather than setting out to
disprove the point from the outset on a theoretical basis.

Ethan's suggestion is something so mindbogglingly simple and obvious,
that I've already done it dozens of times in a number of rooms in the
past...

Regards,
Simon