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Standing waves get their own thread - lucky little blighters!

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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Wed Dec 22, 2004 3:11 am

Hugh Robjohns wrote:
Foz wrote:I would be surprised if the control room monitors used by anyone reading this thread are omni-directional.

You are almost certainly correct in your supposition. However, Dr John Watkinson (general audio guru and digital audio expert) strongly advocates truly omnidirectional loudspeakers. Indeed, his company (Celtic Audio)manufacturers the same for use in both professional monitoring and domestic environments. He also argues strongly that truly omnidirectional monitors are required for surround sound purposes. A lot of people disagree, but his arguments are interesting and well formed nonetheless.

if you have links to omni control room monitors, please drop links, I'd like to see em.

Try ths: www.celticaudio.com

Hugh

A friend of mine recently surprised me by showing me the rear of his incredibly lush-sounding audiophile speakers. The pair of drivers at the front was matched by an identical pair at the rear!

I seem to remember that the front drivers were delayed so that when the speakers were put in their correct positon (a set distance from the rear wall) the reflected and direct sound 'matched up' to give a greater sense of space and depth to the sound.

Interesting concept...
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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Wed Dec 22, 2004 4:25 am

Foz wrote:


Interesting...


Thanks

Interesting is not the word.

RACKMOUNT monitors? :shock:

The bipolar monitors look very interesting as well. Especially the claim to work better when exciting the room's natural resonances.

That has resonance (if you'll exclude the bad pun) with subjects brought up in this thread...

When should we expect reviews in SOS? The claim of a flat frequency response down to 30Hz looks like it's worth investigating.
:)
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Re: Standing waves get their own thread - lucky little blighters!

Postby Paul Woodlock » Wed Dec 22, 2004 5:06 am

Tequila Slammer wrote:
Paul Woodlock wrote:

No it really doesn't work like this. A room of any shape will have resonances between opposing surfaces, parallel or not. These are called room modes, and when sound at the freqeuncy of these modes is generated in the room, standing waves will occour due to the room resonating at those frequencies.

Standing waves do NOT have to be at a normal ( 90 deg ) to the surface. For example a Tangential mode is a resonance between 4 opposing surfaces, where a 90 incidence is impossible. Oblique modes occour becuase of 6 opposing surfaces, again 90 incidence is impossible.

Once a room mode resonance has been excited by energy from the speaker, the resultant standing wave is located throughout the room. This is regardless of speaker position. Although speaker position CAN effect the efficiency of excitement, it has NO bearing on the location or position of the standing wave. It is the ROOM which determines the freqeuncy and position of the standing wave.

Using the Guitar string analogy.....

A guitar string will vibrate at it's resonant frequency(s), regardless of the exact point you pluck the string. However the point of plucking will affect how much each harmonic resonance is excited, and this is why of course, different timbres can be heard by varying the point of plucking. But the point of plucking DOES NOT CHANGE the position of the standing waves in the gutiar string, but does change their amplitude.

The Pickup is the 'listening position' in an electric guitar. Move the position of the pick up and the tonal balance changes. Exactly the same as in a room, where moving the listening position will result in a different tonal balance heard by the listener as he/her travels to different pressure points of the standing wave.

Paul,

Thanks again! That really helped me out.

I hadn't thought of applying resonance to the situation. This adds a whole new concept to the mix - if the room itself is being excited, it is acting as a giant resonant box. It is therefore generating sound at the resonant frequencies, omnidirectionally from each point of the inside surface, I suppose. Yeah?

Sort of. The room doesn't really generate sound in the way you might think. Although I think pedantically this could be argued.

The room is a giant ( or not so giant ) resonant box yes. The standing waves are actually a storage of sound energy. This also takes time. When you playback a mdee freqeuncy from a speaker, there is a Rise Time before the standing wave reaches it's max level. And when you stop playback ( stop feeding the standing wave with energy ) there is a fall time when the energy stored in the standing wave is dissipated due to friction/absorption, etc. So the standing waves not only distort the frequency response, they cause the sound to 'boom' for want of a better word.



This would lead to the generation of standing waves between every pair of surfaces whose distance matched a room node.

It's room MODE not node. I know it was probably a typo :) , but a node is a place of no disaplcement in a standing wave ( anti-node = point of maximum displacement ) So a dangerous typo :)

You don't really have a mode that doesn't match a distance. Although knowing the complexities of acoustics - phew! - I'm sure Eric will come up with a situation where there isn't a room dimension involved ;). But for the purposes of the present discussion....

It's the sufaces which give rise to modes, the frequency of which is determined by the distances between them. It's not only pairs of surfaces either. You can have modes that are resonances between 4 surfaces ( Tangential Modes ), and modes as a result of 6 surfaces ( Oblique Modes ).

I would imagine that a pentagonal room would also have modes as a result of the 5 walls too. but whether that is true or not, is way beyond me.. ERIC!!!!!! :)


Now I see the value of treating the spaces forward, back, above, below and either side of the monitoring position.

The mirror trick I fell in love with as soon as I saw it. Thanks again for pointing me at it.

Your guitar string analogy seems a little strained here however. I imagine a guitar string to equate to one 'ray' of sound - a theoretical single wave path between boundaries. The 'room' would be the guitar itself - or the single body attached to the two ends of the string.

No it's nto strained. Forget about the guitars suond box for a moment. the guitar string analogy I think is good.

nut-string-bridge = Wall-airspring-Wall




How about this - the 'guitar' becomes a simple wooden box and the strings (strung between parallel panels) are all tuned to the same frequency. Plucking one string causes vibrations to travel through the frame and cause sympathetic vibrations in the other strings.

If the frequency of the string is a resonant frequency of the box, the effect will be very marked!

Close or off the mark?

Absolutely! If the resonance of the box equals the strings freqeuncy, then yeah, the box would resonanate like a mother!!

Of course the box will have many resonant modes. And I would think a well designed guitar should ideally resonate at every freqeuncy to produce a full bodied tone at every note without any dead spots.

In fact with Mallet instruments, like a mamrimba, each note has it's own resonant box tuned to the note it lies under. Here's a quaint example Image :) Giz a tune luv! :)


Does this mean room modes are less apparent in more solid structures? A concrete room would vibrate less than a wood and plasterboard structure. Which could help to explain why I'm getting immense amounts of bass at certain frequencies in my current studio (a box room with plaster walls and a wooden floor, where everything on a flat surface jumps around when I walk heavily) and I had almost no bass whatsoever (and quite a flat response) in my last studio - a basement flat with a concrete floor and brick walls.

No in fact it's the other way around. If the boundaries are allowed to vibrate they will ABSORB sound and take some energy away from the standing wave, thus diminishing it. Although a vibrating wall will re-radiate some sound back into the room. And of course it will radiate some sound on the other side of the wall ( again diminishing the standing wave ), and is thus the cause of many a neighbourly dispute.

This is one of the reasons why cars are great places to listen to music, becuase most of the bass simply goes right through the cars body and annoys the outside world - MUWAHAHAHA :)

If you imagine a guitar with a rubber nut and rubber bridge, it might help to visualise this :)

The more the room is soundproofed, the more energy is contained in the room, and the more the excitation of the standing wave.




It still seems to me that the strongest standing waves will be in paths intersecting the speakers between parallel walls - as that is where they're originally being excited and reflections from the walls will enhance the effect.

Second strongest would then be any other paths between parallel walls, as reflections would again enhance.

THEN the standing waves between non-parallel walls would come into play.

A standing wave occours across the whole space of the room between the opposing surfaces. The strongest standing waves are the fundermental axial ( 2 surface ) modes. I know this isn't quite what you meant, but reagrding yur question, I'm pretty sure the max pressure of a standing wave in a room is prety much the same at all anti-nodes.

(I am still a bit sloshed from the office Christmas party ;) )

Did ya photcopy your ass? - and NO dont' post any pics :) ( Mind you I have to admit to posting a picture of the concrete burn I painfully got on my ass while pouring the floating floor, in my studio build dairy - hehe :) )



Oh, and tell me if this gets annoying ;) I feel like I'm really making progress here however - and I could see this being valuable to other readers. :bouncy:

No it's not annoying at all. Apart from being highly interesting anyway, It's also helping me to learn more about it all. I always try to stay within my knowledge bounds, and expect correction if I get things wrong.

But the important thing is raising the subject so the info can filter down through us all.

The Internet Forum IMO is a major leap in the spread of knowledge, but is has it's downsides. And that is the spread of hearsay or false info. In fact that has been one of the main causes of all the upheaval here over the last couple of weeks. And while the methods of debating from myself and others has been a little too uncomfortable for some people. It has certainly been passionate and on a positive note has stimulated some great discussions on the science and application of acoustics.


Anywa...., back to my acoustic treament designs, even though it's gone 4am now :)



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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Thu Dec 23, 2004 12:19 pm

Once again, I feel like I've stepped up a level in understanding. Brilliant.

So, it's the air in the room resonating rather than the structure. Makes sense, I suppose, and yes - that makes the guitar analogy make sense. :) 'Booming' is exactly the right word for what my room did before I put in the absorbers.

I'd still like to know the mechanism of the distribution of energy from the speakers to the rest of the room in this case. (Just 'cause I'm curious). I suppose it's the same physics which relate to any resonating body being energised at the resonant frequency... Is this still pressure wave propagation?

It sounds to me like there might be some other physical properties at work.

I'm also interested in the difference between conventional thinking (solid structures keep more energy in and thus generate more apparent modes) and my experience (a solid structure was completely bass-dead, while the same equipment in a more 'wobbly' structure created lots of bass peaks in the frequency response.)

Initially I thought it was due to the room sizes - my new studio is a lot smaller than the living-room I used to use, and is square. However, the living room in the new house 'booms' as well - and it is of a comparible size to the last one.

I doubt that this problem can be answered without an in depth analysis of all three rooms, materials, contents, etc. If anyone has any ideas though, I'd love to hear them.
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Re: Standing waves get their own thread - lucky little blighters!

Postby Scott R. Foster » Thu Dec 23, 2004 7:01 pm

TS:

Room size undoubtedly has a lot to do with the differences you note... all else being equal, different sized rooms will resonate differently. As to boundary stiffness, both structures probably have appreciable acoustic "wobble". For example a plasterboard wall might be very absorptive at 250 Hz, but very reflective at 175 Hz.

Bottom line.. even knowing next to nothing about the dimensions, construction or contents of the two rooms, both rooms are probably in need of significant absorptive treatment to even out colorations caused by coincident room modes [a function of room shape]... uneven absorptive properties across the band [a function of boundary and contents absorptive properties]... and acoustic artifacts of low modal density in the lower part of the band [a function of room size - large rooms have lots of modes low in the band, small rooms don't].

It takes a fairly large room with fairly stiff walls, floors, and ceilings and some well proportioned dimensions to avoid all those problems.

In all likelihood, both rooms suffered from a collection of the abovedescribed problems to different levels of expression... at least, that'd be my guess.
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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Wed Dec 29, 2004 12:57 pm

Paul Woodlock wrote:
No in fact it's the other way around. If the boundaries are allowed to vibrate they will ABSORB sound and take some energy away from the standing wave, thus diminishing it. Although a vibrating wall will re-radiate some sound back into the room. And of course it will radiate some sound on the other side of the wall ( again diminishing the standing wave ), and is thus the cause of many a neighbourly dispute.



Foz wrote:TS:

It takes a fairly large room with fairly stiff walls, floors, and ceilings and some well proportioned dimensions to avoid all those problems.

OK, I'm confused. Are hard walls bad or good for standing waves - or room modes?

I'm beginning to like Ethan's way of thinking on this issue - thinking of room modes as standing waves has caused me a great deal of confusion, while thinking of them as room resonances makes more sense...

OK, To re-iterate, flat 1 had two rooms - one large, one small. The bass was almost non-existant, and I didn't hear the effects of nodes and anti-nodes while walking around the rooms. The walls were very hard indeed.

The house has two rooms, of similar dimentions to the flat. The bass is large ad boomy. When untreated, walking around both rooms gives very obvious node and anti-node effects. The walls are really quite flimsy by the feel of them, and the floorboards are loose enough that walking across the room makes objects vibrate on all flat surfaces. Window sizes and placements are similar.

So what's going on?
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Re: Standing waves get their own thread - lucky little blighters!

Postby thefruitfarmer » Wed Dec 29, 2004 3:35 pm

Tequila Slammer wrote:

The house has two rooms, of similar dimentions to the flat. The bass is large and boomy. When untreated, walking around both rooms gives very obvious node and anti-node effects. The walls are really quite flimsy by the feel of them, and the floorboards are loose enough that walking across the room makes objects vibrate on all flat surfaces. Window sizes and placements are similar.

So what's going on?

The walls and floor could be resonating in sympathy which may then mean they act as a sound box (= problem).

A heavy and solid wall or floor is less likely to vibrate.
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Re: Standing waves get their own thread - lucky little blighters!

Postby Eric Desart » Wed Dec 29, 2004 4:44 pm

Tequila,

It can be good to check that besides the traditional modal issues, objects or panels are resonating.

You can do that by sending a sweep in the room from low to high.
Anything has its natural resonances. It doesn't matter that much if they are damped enough.
With a sweep you can easier localize undamped resonances. Loose, low damped things start clattering/rambling when excited with the corresponding frequency.

Such things should be fixed, since they will screw the sound anyhow.
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Re: Standing waves get their own thread - lucky little blighters!

Postby Scott R. Foster » Wed Dec 29, 2004 5:18 pm

thinking of room modes as standing waves has caused me a great deal of confusion, while thinking of them as room resonances makes more sense


TS:

How does it help to pretend that a "room resonance" is something other than a "standing wave"?

Wait.. don't answer that. I'll agree that as long as the discussion is solely about grasping a rudimentary idea of what changes to a room will help achieve a certain result in modal behavior we don't need physics. In that event, any analogy will suffice [provided it remains valid to real physics]. But let's not let using analogies to physics as a shortcut allow anyone to pretend they have changed the laws of physics... or "discovered" something new. That sort of silliness just breeds misconception and wastes folks time AND money.

It's pointless to argue over how one should look at a physical phenomena if the only goal is to grasp a general rule of cause and effect... it doesn't matter in that context... but it is silly to pretend that looking at something differently changes what it really is.

Room modes result from standing waves... but that don't mean you have to learn to visualize wave behavior to understand how to manipulate room modes. Calling room modes something else besides standing waves [Dragon Farts for example], and picturing the physical elements that give rise to them in some creative way that works for you as you go about trying to control them does nothing to change the real causes or limit your ability to make effective changes [though it may help you get your project completed and move on to other things].

We could forget waves altogether. Maybe we should.. it sounds like that would help you in some way... and I have no objection with that goal.

We could just say the room's resonances are driven by interior dimensions and the reflectiveness of the surfaces [ceiling/floor/walls] and taken together they act like a set of large water jugs spread out on the floor and filled to different levels so that the jugs hum at different notes... and its a good thing if the levels in the jugs vary... so you get a nice even mix of tones... none dominating. Maybe, that is enough for practical purposes of understanding how to address room modes when they cause problems... as long as you don't let the analogy drive you into misconceptions on the real physics behind the problem.

A few points on those humming jugs:

1) The lower toned jugs are the worrisome ones - how high up the band you need to be concerned is a function of modal density. If you have 50 jugs in a given octave, they tend to drown each other out, no particular tone dominates... the more jugs per octave the better. Small rooms have low modal density. The problem is worst low in the band, and the smaller the room the higher on the band the problem will reach. So small rooms are more prone to modal problems, and they are prone to these problems at higher frequencies.

2) Modes arise from a large set of dimensions - not just the distances between parallel surfaces [axial modes] - so there are more than 3 of them [and their harmonics]. Instead there are dozens of modes below critical levels of density for any given room. Choosing to look at only the axials is working in the blind. OTOH the axials are the biggest jugs [the loudest] so problems with this set of jugs can cause the worst problems... but happily axials are the easiest to alter [example if the front to rear wall axial matches the ceiling axial, then a broadband absorptive ceiling and a large diffusion array on the rear wall will go a long way to removing the problem].

3) By shifting just one dimension of the room you alter the level in a large number of jugs - this is trivial if you think about it BEFORE the room is built. Best to do your jug level juggling before you build.

4) Broadband absorption diminishes the loudness of all the tones - and all tones exist in corners - broadband absorption in corners will turn down all of a room's resonances - a good place to start.

The point of the above is to agree that we can talk about room modes without talking about wave behavior... and cite a series of examples... but be careful you don't let the analogy become the topic. The problem for me arises when someone wants to say something incorrect about the physics in the context of an analogy, and then insists the analogy is the proper context for discussion... at some point to get the whole picture, and engage in a real debate of all the elements, you have to drop the analogies and talk about waves.

Does that mean it is necessary to dispense with analogy in order for the average person to wrestle with room modes in their home studio? I don't think so, but if we are going to debate various points on the physics behind the cause and effect of room modes, then I think its time for the analogies to go away. And if you want to participate in that discussion... then you need to grasp that room modes ARE standing waves... anything short of that and you're just talking into your hat.

My $0.02
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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Thu Dec 30, 2004 10:57 am

thefruitfarmer wrote:
Tequila Slammer wrote:

The house has two rooms, of similar dimentions to the flat. The bass is large and boomy. When untreated, walking around both rooms gives very obvious node and anti-node effects. The walls are really quite flimsy by the feel of them, and the floorboards are loose enough that walking across the room makes objects vibrate on all flat surfaces. Window sizes and placements are similar.

So what's going on?

The walls and floor could be resonating in sympathy which may then mean they act as a sound box (= problem).

A heavy and solid wall or floor is less likely to vibrate.

That was my theory. It seems to be accepted theory that hard walls will reflect more bass however.
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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Thu Dec 30, 2004 10:58 am

Eric Desart wrote:Tequila,

It can be good to check that besides the traditional modal issues, objects or panels are resonating.

You can do that by sending a sweep in the room from low to high.
Anything has its natural resonances. It doesn't matter that much if they are damped enough.
With a sweep you can easier localize undamped resonances. Loose, low damped things start clattering/rambling when excited with the corresponding frequency.

Such things should be fixed, since they will screw the sound anyhow.

Brilliant idea, thanks! :lol:
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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Thu Dec 30, 2004 11:11 am

Foz wrote:
thinking of room modes as standing waves has caused me a great deal of confusion, while thinking of them as room resonances makes more sense


TS:

How does it help to pretend that a "room resonance" is something other than a "standing wave"?

Wait.. don't answer that. I'll agree that as long as the discussion is solely about grasping a rudimentary idea of what changes to a room will help achieve a certain result in modal behavior we don't need physics. In that event, any analogy will suffice [provided it remains valid to real physics]. But let's not let using analogies to physics as a shortcut allow anyone to pretend they have changed the laws of physics... or "discovered" something new. That sort of silliness just breeds misconception and wastes folks time AND money.

It's pointless to argue over how one should look at a physical phenomena if the only goal is to grasp a general rule of cause and effect... it doesn't matter in that context... but it is silly to pretend that looking at something differently changes what it really is.

Room modes result from standing waves... but that don't mean you have to learn to visualize wave behavior to understand how to manipulate room modes. Calling room modes something else besides standing waves [Dragon Farts for example], and picturing the physical elements that give rise to them in some creative way that works for you as you go about trying to control them does nothing to change the real causes or limit your ability to make effective changes [though it may help you get your project completed and move on to other things].

We could forget waves altogether. Maybe we should.. it sounds like that would help you in some way... and I have no objection with that goal.

We could just say the room's resonances are driven by interior dimensions and the reflectiveness of the surfaces [ceiling/floor/walls] and taken together they act like a set of large water jugs spread out on the floor and filled to different levels so that the jugs hum at different notes... and its a good thing if the levels in the jugs vary... so you get a nice even mix of tones... none dominating. Maybe, that is enough for practical purposes of understanding how to address room modes when they cause problems... as long as you don't let the analogy drive you into misconceptions on the real physics behind the problem.

A few points on those humming jugs:

1) The lower toned jugs are the worrisome ones - how high up the band you need to be concerned is a function of modal density. If you have 50 jugs in a given octave, they tend to drown each other out, no particular tone dominates... the more jugs per octave the better. Small rooms have low modal density. The problem is worst low in the band, and the smaller the room the higher on the band the problem will reach. So small rooms are more prone to modal problems, and they are prone to these problems at higher frequencies.

2) Modes arise from a large set of dimensions - not just the distances between parallel surfaces [axial modes] - so there are more than 3 of them [and their harmonics]. Instead there are dozens of modes below critical levels of density for any given room. Choosing to look at only the axials is working in the blind. OTOH the axials are the biggest jugs [the loudest] so problems with this set of jugs can cause the worst problems... but happily axials are the easiest to alter [example if the front to rear wall axial matches the ceiling axial, then a broadband absorptive ceiling and a large diffusion array on the rear wall will go a long way to removing the problem].

3) By shifting just one dimension of the room you alter the level in a large number of jugs - this is trivial if you think about it BEFORE the room is built. Best to do your jug level juggling before you build.

4) Broadband absorption diminishes the loudness of all the tones - and all tones exist in corners - broadband absorption in corners will turn down all of a room's resonances - a good place to start.

The point of the above is to agree that we can talk about room modes without talking about wave behavior... and cite a series of examples... but be careful you don't let the analogy become the topic. The problem for me arises when someone wants to say something incorrect about the physics in the context of an analogy, and then insists the analogy is the proper context for discussion... at some point to get the whole picture, and engage in a real debate of all the elements, you have to drop the analogies and talk about waves.

Does that mean it is necessary to dispense with analogy in order for the average person to wrestle with room modes in their home studio? I don't think so, but if we are going to debate various points on the physics behind the cause and effect of room modes, then I think its time for the analogies to go away. And if you want to participate in that discussion... then you need to grasp that room modes ARE standing waves... anything short of that and you're just talking into your hat.

My .02


Well, that didn't work. I was hoping that that comment would prompt a discussion about the physics of room modes, and why they behave the way they do.

Everything you've said is very useful practical stuff, and thanks :) but I'm interested in the physics now. I want to know why thinking about room modes as waves of any kind gets me nowhere.

Talking about jugs and dragon farts isn't helping ;)

Thing is, I thought I knew about waves. So, either I'm missing certain knowledge about wave theory (or misapplying what I do know) or we're dealing with a physical property that is different to or supplemental to wave theory.

I want to know which, and learn about it.

Does anyone know any good books?
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Re: Standing waves get their own thread - lucky little blighters!

Postby thefruitfarmer » Thu Dec 30, 2004 5:39 pm



"Does anyone know any good books?"



Foyles Bookshop in the Charing Cross Road have a science department. I found a physics graduate working there recently who was all happy to chat about maths and help me find a suitable maths text book. I still don't have that much of a scientific mind though..... ;)

Re standing waves try this.

It is the size of the room (the modes) which determines at what frequencies the standing waves will occur at.

I think of it as being when the wavelength of the sound wave is such that it fits neatly in to the size of the room and the reflected wave interacts with the original wave in such a way as to result in the peaks and nulls within the room.

The formation of standing waves is a problem because it means that you may not be hearing the music as it really is. There could be more bass than you hear if you are sitting in a null area or less if you are sitting in a peak area.

So, what people do when building studios is to install absorption to prevent the sound reflecting around the room. If the room cannot reflect the standing waves will not occur. Then you can hear the music without the colouring effect of the room which does make an incredible difference.
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Re: Standing waves get their own thread - lucky little blighters!

Postby Tequila Slammer » Fri Dec 31, 2004 10:40 am

Thanks, Fruit Farmer. Foyles is a probably good place to go - although the temptation to pop over the road to Turnkey may be too great. ;)

I was hoping someone might know a particularly good book on the subject.

As it goes, I'm up on that bit of the theory. I'm just confused about the property of standing waves/room modes that makes them independent of speaker position. The bit that makes treating parallel walls around the monitoring position a good idea. If anyone can explain the physics of that bit, or point me at a thread that does, please do. If anyone can point me at a book that goes into that kind of detail, please do.

I've got as far as 'the air in the room is resonating' but I lack knowledge concerning the difference between the mechanics of a pressure wave in a body of air and the mechanics of a resonating body of air.
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Re: Standing waves get their own thread - lucky little blighters!

Postby Ido » Fri Dec 31, 2004 10:42 am

="Tequila Slammer.

Does anyone know any good books?


I think the best for this (and all around) is the Everest Master Handbook.
His coverage of standing waves to room modes is the most clear and understandable I ever saw [it's also cheap $].
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