Why do Lows act as Waves and Highs act like Rays?

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Why do Lows act as Waves and Highs act like Rays?

Postby lex » Sat May 20, 2006 7:15 pm

After reading and observing about sound basics (frequency, velocity, wavelength, compressions, rarefactions, rays, waves, amplitude, intensity), and its behavior in different circumstances (diffraction, diffusion, reflection, refraction, interference), I am left with some fundamental questions.

In distant rooms the bass notes are more prominent because their longer wavelengths are readily diffracted around corners and obstacles.

(pg 245 Master Handbook of Acoustics)

Ok, we are all familiar with this type of phrase but I'm wondering, why? I know after reading this excellent book that sound at different frequencies behaves differently depending on which range it falls. (pg 324 of the Master Handbook of Acoustics is excellent)

Here are a couple of paragraphs from Everest on these differences:

(pg 236 Master Handbook of Acoustics)
Below 300-400 Hz, sound is best considered as waves (chapter 15 expounds on this). Sound above 300-400 Hz is best considered as traveling in rays. A ray of sound may undergo many reflections as it bounces around a room. The energy lost at each reflection results in the eventual demise of that ray. Even the ray concept is an oversimplification: Each ray should really be considered as a "pencil" of diverging sound with a spherical wavefront to which the inverse square law applies.

The mid/high audible frequencies have been called the specular frequencies because sound in this range acts like light rays on a mirror. Sound follows the same rule as light. The angle of incidence is equal to the angle of reflection, as in Fig. 10-2.


Why do the high frequencies act as rays and why do the low frequencies act as waves? The frequency only determines the amount of wavefronts or compressions per unit of time but the wavefronts are the same(originate at a source and spread out in spherical fashion) for any sound. So why is it the wavefronts of low sounds can go around objects while the wavefronts of high sounds are reflected? Is this a difference of energy that it comes down to? The wavelengths are afterall the distance between the compressions or rarefactions and not a measurement of the wideness of a wave.

Can someone help me understand this or tell me where I can find this information because I have been reading and not finding anything except general explanations?

I've also posted this question in this forum if you'd like to answer there instead, thanks:
http://www.johnlsayers.com/phpBB2/viewt ... 4441#44441
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Postby J.F.Oros » Sat May 20, 2006 7:40 pm

Not a full answer, sorry, just a (key) observation :

It's about the soundwave lengths in raport to usual objects and room dimensions, and also in raport to source dimensions (usually speaker enclosures). For the audio frequency range (20 Hz - 20 kHz) the wavelengths varies from aprox. 17m to 1,7 cm, so the LF waves can "ignore" the objects whereas the HF waves are affected (reflected, difracted, etc.) by them.
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Postby lex » Sat May 20, 2006 8:24 pm

Thanks for your reply, I'm looking for something more in depth though.

The wavefront is not linear and finite, it is curved and infinite.  So why is the wavelength which strikes perpendicular to the object the determinant of why a wave can go around an object?
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Postby jonessy » Sat May 20, 2006 9:08 pm

Lex,

Diffraction is a physical property, and can be understood intuitively by looking at other types of mechanical waves.

Imagine a small boat in the middle of the ocean.
Most water-waves get diffracted around this boat, since it is small relative to their wavelength.

Now, let's replace our small boat with one huge aircraft-carrier.
You will notice that some waves are still diffracted around the ship (the ones with very-very-very big wavelength), but many waves that could diffract around the small boat, are reflected by our new huge-ship since their wavelengths are smaller relative to the ship's dimensions.


The wavefront is not linear and finite, it is curved and infinite.  So why is the wavelength which strikes perpendicular to the object the determinant of why a wave can go around an object?


You are thinking of the term 'wave' in a sense of an object, and that's a wrong point of view.
The 'wave' is simply a pressure-wave within a springy medium (such as air).
The air can 'go around' an object, since it's air.
The question is not whether air can diffract around an object, but whether the changes in air-pressure can...
And this relies on wavelength.
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Postby Bob » Sat May 20, 2006 9:40 pm

Guessing.
I thought that all waves had a certain directionality and momentum and inertia (not the right physics word).

In the case of HF, when they come out of a speaker, the wavelength is so small that any sound folded to the side gets trashed by the next vibration of the speaker, because even a tweater is fairly wide compared to the wavefront. The center of the tweater has more pressure than the sides of the tweater, because the sides are contributing to the center, and like a gun (a bullet is an object not a wave, so ?) the more pressure behind the bullet the further it goes.

In the case of LF, when they come out of a speaker, the wavelength is not only larger than the woofer it's larger than the speaker, so when it folds around and goes everywhere, the next vibration of the speaker doesn't collapse the sideways going fronts because the woofer is too slow.



Guesses aside, even in an anecoic chamber, you can stand behind a speaker and still hear HF. So it doesn't only go one direction, just more of it.

Bose polar radiation patterns (off axis response, directivity patterns ) plots at 125hz, 250hz, 500hz, 1khz, 2khz, 4khz, 8khz, 16khz  http://www.bose.com/pdf/pro/polar_plots/fs_6/pp_fs6.pdf
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Postby bert stoltenborg » Sat May 20, 2006 9:58 pm

Bob wrote:
In the case of HF, when they come out of a speaker, the wavelength is so small that any sound folded to the side gets trashed by the next vibration of the speaker, because even a tweater is fairly wide compared to the wavefront. The center of the tweater has more pressure than the sides of the tweater, because the sides are contributing to the center, and like a gun (a bullet is an object not a wave, so ?) the more pressure behind the bullet the further it goes.

In the case of LF, when they come out of a speaker, the wavelength is not only larger than the woofer it's larger than the speaker, so when it folds around and goes everywhere, the next vibration of the speaker doesn't collapse the sideways going fronts because the woofer is too slow.


I'm not quiet with you Bob.
Could you rephrase this?
a typical tweeter is 20 -25 mm, so no very large compared to a 17 kHz wave.
I don't understand what you mean with this folding and trashed stuff.
:D
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Postby bert stoltenborg » Sat May 20, 2006 10:09 pm

jonessy wrote:Lex,

Diffraction is a physical property, and can be understood intuitively by looking at other types of mechanical waves.

Imagine a small boat in the middle of the ocean.
Most water-waves get diffracted around this boat, since it is small relative to their wavelength.

Now, let's replace our small boat with one huge aircraft-carrier.
You will notice that some waves are still diffracted around the ship (the ones with very-very-very big wavelength), but many waves that could diffract around the small boat, are reflected by our new huge-ship since their wavelengths are smaller relative to the ship's dimensions.


The wavefront is not linear and finite, it is curved and infinite.  So why is the wavelength which strikes perpendicular to the object the determinant of why a wave can go around an object?


You are thinking of the term 'wave' in a sense of an object, and that's a wrong point of view.
The 'wave' is simply a pressure-wave within a springy medium (such as air).
The air can 'go around' an object, since it's air.
The question is not whether air can diffract around an object, but whether the changes in air-pressure can...
And this relies on wavelength.


See air as a bunch of little balls attatched to rubber bands. When you hit the ball it moves until the rubber band pulls it back. But it hits the next ball, and that hits the next ball.
So the air is only moving around an equilibrium, the particles stay in fact in place, but the wave travels because every ball hits the next .
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Postby Eric Desart » Sun May 21, 2006 7:46 am

Nice vizualisation Bert.

The question is still the width.
One could indeed say that a wave in air has a width not only a length (wavelength versusus frequency and velocity).

Imagine Bert's explanation.
Now see that those rubber bands are not only longitudinal in the propagation direction of the wave but also sideways.
You can not have a ball moving back and forth without them pulling on the balls left and right to them.
Hence a wave extends outwards (not the same as propagation direction) traverse to propagation direction.

This is no nice boundary however but a gradual thing.
Therefore in a room where the wavelength becomes large (read: hence wave becomes wide but with gradual effect) in function of the wall, or object boundaries, you can not see a wave anymore as lines propagating in a purely longitudinal direction.

It's a bit like an elastic front.  If you block part of it (screen, walls) the rest of the wave will be influenced as well,
and it's related like also jonessy told with the relationship of the magnitude of the object versus the wavelenght.

If you put something large in its path you block the whole wave (that ship). If you put something small in its path that elastic front wants to continue what it was busy with and restores itself after it passed the object, just causing a small deformation in the wave at the position of the object.

That's also what the edge effect of absorption is about.  You block part of the wave by absorption, but the part outside the absorber is elastically connected to that.  Hence the effect of the absorption extends outside the physical boundaries of that absorber. And also here that's related with the wave length (read: wave width).
The edge effect of absorbers still works when the edges of the absorber are reflective.
It's the difference in impedance on part of that same wave front causing to scramble this wave behavior.
Hence the net "classic/EW/axiom" that it is linear edge surface increase related, wich is a frequency independent constant is wrong.

Have a look here:
http://www.realtraps.com/art_measure.htm
Underneath the corner absorber picture in the left green bar down the page.
RealTraps wrote:So in practice, a two-foot corner wedge like this provides only 65 percent of the absorption claimed.
 :wink:  Quiet accidentally the picture shows some typical (competing) foam absorber.
This above quote, in the used context, is plain fantasy in a pseudo scientific cloth.  A MiniTrap in a corner will show as much edge effect, not dependent of the edge surface.

It is this wide front behavior that causes Everest to distinguish between the high frequent ray behavior (wave lengths, read widths are small versus walls and objects, hence geometric acoustics applies) and the low frequent wave behavior were waves become large versus bounderies, edges, objects, etc.
Hence this is no nice border with a cutoff frequency between both ranges, but is related with wave length versus object sizes (see jonessy nice explenation as well)

Eric
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Last edited by Eric Desart on Sun May 21, 2006 12:37 pm, edited 5 times in total.
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Postby bert stoltenborg » Sun May 21, 2006 9:37 am

Thanks guys.

I like this way of thinking about acoustical mechanics.
Makes thinks so much clearer than only saying "a gassous medium is elastic" and then throwing in a bunch of math.
:D
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Postby jonessy » Sun May 21, 2006 10:15 am

A few more points to look at:

We know that directionality characteristics rely on wavelength\width and on diffraction around objects.
Now, let us consider a perfect mono-pole source (omnidirectional for all frequencies) in a perfect acoustic free field (no boundaries, no objects, nothing, nada, gurnisht, zip, kloom).

In this case, NOTHING gets diffracted since there is nothing to diffract around, so one may say that 'lows' and 'highs' have equal directionality.
Bob - this has nothing to do with loudspeaker radiation patterns since in this example all frequencies are projected evenly in all angles of incidence from our monopole source.

But this is NEVER the case. We always have some boundaries that in a sense can be regarded to as objects.

IMHO Crossover freq. between 'directional' and 'non-directional', hence has something to do with the characteristics of the discussed acoustical space.

In smaller rooms and more diffuse rooms, it is easy to distinguish between directional and non-directional frequencies.
The larger the space becomes, the lower this 'crossover' freq. becomes, so the 'lows' become more directional respective to the dimensions of the space itself.
Hence we categorize large spaces as 'geometric' - most audible frequencies ARE directional, wheras in smaller spaces most of the audible low-range is indirectional.

AFAIK, A part of schroeder's freq. equation relies on this assumption.
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Postby Eric Desart » Sun May 21, 2006 10:17 am

Bert,

And this also relates to your not working Bertse bass traps.
:mrgreen:  Aren't you going to commercialize those? They are unique ......

You're putting a resistance on part of a modal wave front, searching for the position where it has most effect.

But the rest of that front continues to like playing mode. Hence you must pull, push hard enough on limited part of that front in order to stop or diminish that frequency wanting to play mode.
Hence you search for the most effective spot where you can criple that front the most , and if not working good enough you must fight a larger area of that front.

Eric
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Postby Ido » Sun May 21, 2006 11:50 am

can LF project as non-plane? in a narrow pattern, somewhat like rays? in a natural way?
I'm trying to envision interaction between different LF, sort of like in combfiltering.
(I do realize the significance of relativity in this matter, I mean in a human scenario, not in outerspace).

Eric, your description above was great.
you're finally learning to talk to those of us with the more limited capabilities  :twisted:.
I know you always try. I't's not your fault you're too smart  :mrgreen: .

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Postby Eric Desart » Sun May 21, 2006 12:01 pm

Jonnesy,

It's not directly clear to me, but their is certainly something to be said for Bobs approach.

A high frequent practical source is easily directional, a low frequent source not, independent of the space.

That's something to sleep about, but I tink it's related with time and displacement.
For the same sound pressure the particle displacement in air is inverse linear related with frequency.
Hence, at the same pressure, the displacement of air particles at 100 Hz is 100 times larger than the displacement at 10000 Hz
(hope this is correct now).

In that sence the traditional representation of longitudinal waves by traverse waves, to have a better view on amplitude and wavelength versus frequency and velocity can be a bit confusing, in the sence that you can easily misinterpret the amplitude as some kind of, or representing also a displacement measure.

You can SEE the displacement of subwoofer cones. You can't see the much smaller, much faster tweeter displacement.

Its this much slower in frequency and larger displacement, which extends further sideways. (inertia)

But as said. I have to sleep about it.

Eric
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Postby jonessy » Sun May 21, 2006 12:46 pm

Eric Desart wrote:Jonnesy,
It's not directly clear to me, but their is certainly something to be said for Bobs approach.


Never said there isn't. :)
And I'm pretty sure I didn't understand Bob's explanation completely.

But 'large' and 'small' are relative terms.
One can say that for lower frequencies the displacement of air particles is bigger, than for higher frequencies.
This is correct, but should be compared to the size of the free-path in which the wave propogates.

If the path is small, the displacement is limited for certain frequencies.
The larger the path becomes, more and more (lower) frequencies with higher wavelengths can freely propogate.

I guess what I'm trying to say here, is that physical directionality characteristics may be hardly enough to determine the true directionality of the wave.
One should consider the propogation medium and it's boundaries as an important factor when deciding on this 'crossover' frequency.
...And this frequency may be derived from the physical characteristics of the wave itself in regards to the characteristics of the discussed space.
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Postby Eric Desart » Sun May 21, 2006 2:35 pm

jonessy wrote:But 'large' and 'small' are relative terms.
One can say that for lower frequencies the displacement of air particles is bigger, than for higher frequencies.
This is correct, but should be compared to the size of the free-path in which the wave propogates.

If the path is small, the displacement is limited for certain frequencies.
The larger the path becomes, more and more (lower) frequencies with higher wavelengths can freely propogate.


johnessy I don't/didn't dispute the relationship with room sizes, as you saw before. I do/did agree with your explanations (not sure about Schroeder, which based his stuff on modal density and overlap)

The original question was why?  What makes a low frequency not behave as a ray?  What makes that it behaves as having a width as well? Behave as a front?
The results in function of a room, screens etc. are known and described, mostly vaguely, which is why Lex asked, referring to Everest.

I think I misunderstand you partly here
You are aware that this displacement of air particles ranges between mini fractions and fractions of a mm?
You must go low frequent already with very high sound pressure to exceed one mm.
:)  That path must become very small.
.
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Postby Terry Montlick » Sun May 21, 2006 6:11 pm

Wave diffraction is complicated, pure and simple! :bang  See for example:

http://scienceworld.wolfram.com/physics ... ction.html

I don't know of a good simplifying visualization that works under all circumstances, but picturing all the edges of an object as re-radiating the wave comes the closest, I think.

Diffraction dominates whenever wave obstruction feature sizes are around the same as or smaller than a wavelength. Then, the wave cannot cast a clean shadow. But when wavelengths are tiny compared to object features, the wave does cast a clean shadow (the interference fringes at the edge are insignificant), just like a particle would do.

For example, one can  block outdoor high frequencies with a wall or hillside which is tall compared to the corresponding wavelengths. But low frequencies -- forget about 'em! They easily diffract around the obstructions.

Regards,
Terry
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Postby Eric Desart » Sun May 21, 2006 7:15 pm

Terry Montlick wrote:Wave diffraction is complicated, pure and simple! :bang

I second this  :bang  :bang    ( :mrgreen: I'm the second)
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Postby jonessy » Sun May 21, 2006 9:01 pm

Eric Desart wrote:
Terry Montlick wrote:Wave diffraction is complicated, pure and simple! :bang

I'll second this  :bang  :bang    ( :mrgreen: I'm the second)


I'm third! Hip Hip!  :bang  :bang  :bang  :)
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Postby J.F.Oros » Sun May 21, 2006 9:06 pm

Hey Jonessy, you don't wanna do that : it's a three leaf system !  :mrgreen:
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Postby jonessy » Sun May 21, 2006 9:13 pm

Okay folks,
This is a little OT, but I'm going to abuse this thread with something I've been looking for for a while.

Next semester I'm assigned to teach a course called "intro to acoustics for musicians", which is basically the same as "intro to acoustics for everyone", only without the math...  :twisted:
I'm working my ass off trying to think of methods to explain relatively complicated stuff and a plain, non-mathematical way (such as oranges and apples instead of sigmas and integrals... Just kidding  :8 Not THAT simple).
Can anyone think of a creative and simple explanation of the relationship between wave frequency and wave energy?
Or for the sake of it, why is wave energy frequency-dependant.
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