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how to calculate spl drop off rate?

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Abe The Babe View Drop Down
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    Posted: 17 September 2011 at 12:31am
  Hi, this is my first post. I've been reading this forum and other articles on speaker building all summer and think I'm ready to start building some speakers. Luckily a friend of mine is a cabinet builder, who's interested in giving me a hand, so I should be off to a good start.
 
 A guy I know built a gigrig this summer and has a very limited budget (€3000ish) for speakers. I will probably be using the rig, so I want the speakers to be as suitable for the application as possible (mostly traditional Irish music, so not too loud, mostly fiddles, whistles, acoustic guitar, accordion, vocals and bodhrains)
 
 I've been thinking of building 4limmer horns, http://lsv-achenbach.de/s/lautsprecher/limmer/P3_4.jpg - http://lsv-achenbach.de/images/lautsprecher/limmer/P3_4.jpg if I can get him to stretch the budget that far.
He already has a few kme amps from the rig he started with, (2x18" KME subs, with 2x rubbish 15" auna tops and 2x old cheap 15" dynacord tops, obviously bought before I met him)
 
 What I'm wondering is how do you calculate the drop off in spl (not sure how thats supposed to be worded) over a given distance is it based on dispersion? If I knew this it would be alot easier to work out what speakers are suitable.
 
 Hope this isn't a stupid question that has been asked loads of times.
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Abe The Babe View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Abe The Babe Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 12:32am
Also, If anyone has other suggestions on speaker designs it would be really appreciated. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Saturnus Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 12:49am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Abe The Babe Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 1:03am
Surely the distance law is not the same for direct radiating speakers and horn loaded. Otherwise how are long throw speakers able to throw any further?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Saturnus Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 1:14am
Originally posted by Abe The Babe Abe The Babe wrote:

Surely the distance law is not the same for direct radiating speakers and horn loaded.

There's no difference. That's why it's called the Distance Law Wink

 

Originally posted by Abe The Babe Abe The Babe wrote:

Otherwise how are long throw speakers able to throw any further?

Not sure what you mean by long throw speaker here. If you mean that some speaker have large cone displacement then I don't see the relevance. And if you mean that horn speakers have "throw" that allow them to break the laws of physics, then no, it doesn't exist. It only appears that way because horn speakers radiate over a larger area so the volume appears lower than it should be closer to the speakers, which is inverse mistaken to mean they are louder farther away than direct radiating speakers.



Edited by Saturnus - 17 September 2011 at 1:22am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Abe The Babe Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 1:28am
http://www.voidaudio.com/pdf/lffaq.pdf%20 - http://www.voidaudio.com/pdf/lffaq.pdf 

Edited by Abe The Babe - 17 September 2011 at 1:30am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Saturnus Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 1:36am

I already explained this above. It's the difference in radiation area. If you have 2 cabs. One a horn enclosure and one a direct radiator enclosure, and the mouth area of the horn is the same as the SD of the dynamic driver then drop off at distance will be 100% percent the same as dictated by the distance law.



Edited by Saturnus - 17 September 2011 at 1:47am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Abe The Babe Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 1:45am
Ok I understand you now. Thanks
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Abe The Babe Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 1:52am
Ok I understand you now. Thanks. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Steve_B Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 2:44pm

Consider a point as a small oscillating sphere. The sphere puts out a series of pressure waves which move away from the source as increasing spheres. Consider just one wave. Once the wave has left the source it can’t gain any extra energy.  Therefore as it moves away from the source the energy is spread over an increasing area.  For a sphere the surface area increases with the square of the radius so each time you double the distance from the source (or radius) the surface area increases by a factor of four.

In acoustic books it is referred to as the sound intensity and is the rate at which sound energy is transmitted through a unit area. Because the area increases by a factor of four for every doubling of distance the intensity decreases by the same amount. A factor of 4 is the same a 6 when expressed in terms of dB. This is where the 6dB fall off comes from.

If you now put the sound source in a wave guide so that the sound radiated over a restricted portion of the sphere, the actual intensity will increase but the fall off will still stay at 6dB per doubling of distance because the area that the sound radiates into is still increasing spherically.

If the sound radiates cylindrically, as line arrays claim to do, the area that the sound radiates into increases on proportion to the radius. Double the distance and the area doubles. This corresponds to a 3dB fall off.

There is no such thing as throw really, but technicians referred to the technique of placing a narrow dispersion horn high up, so that those close up were off axis, as throwing the sound over the heads of those at the front.

If your sound source is in a room the above only partially applies. The intensity of the direct sound sill decreases at 6dB for each doubling of distance, but at some point the sound hits the walls and creates a reverberant sound field. The level of the reverberant sound is constant throughout the room. The sound that you hear therefore comprises of the direct sound and the reverberant sound. Close up to the source, the direct sound dominates, but at some point, as you move away from the source, the direct sound and reverberant sound are the same level. This is usually referred to as the critical distance. Once you get beyond the critical distance the reverberant sound dominates and the sound level remains fairly constant.

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Post Options Post Options   Thanks (0) Thanks(0)   Quote Abe The Babe Quote  Post ReplyReply Direct Link To This Post Posted: 17 September 2011 at 4:11pm
Thanks Steve, that was very informative. Does using a wave guide on say a 15" increase spl compared to leaving it direct radiating?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Steve_B Quote  Post ReplyReply Direct Link To This Post Posted: 18 September 2011 at 1:59pm

As long as the wave guide is large enough it will control the dispersion pattern and possibly increase the on axis spl. Large is determined by the wavelength of the sound at a particular frequency. As a rough rule of thumb the mouth dimensions of a wave guide should exceed one wavelength of the sound transmitted for it to influence directivity. 15” loudspeakers tend to be used at lower frequencies which means that the waveguide will need to be quite large Additionally, because the dispersion angle is determined by the angle between the walls of the guide, the narrower the dispersion angle the longer the wave guide needs to be to achieve the required mouth dimension.

 

The following picture shows a graph of the directivity index of a typical 12” loudspeaker.

The directivity index is expressed in dB and is the increase in on axis spl over the level that would be achieved if the sound was being radiated omnidirectionally. For a given frequency a 15” speaker would have a slightly increased directivity index compared to the 12". For comparison, a 90 x 40 degree horn will have a directivity index of about 11.

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