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First Reflection Point Formula

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I had run into this formula in the past but can no longer remember the source. I thought I had read it on the RPG site, but can't seem to find it there, if it was even the correct source to begin with. Anyway this was a formula to calculate where the first reflection points would be located in the room. I believe it used the distance of the listening position to the side wall and the distance of the listening position to the speakers. I have tried the mirror test and I'm not sure it's identifying the position correctly. It appears to me the first reflection point is too close to the speaker using this test. Can anyone provide some assistance. Thanks in advance.

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Re: First Reflection Point Formula - David Aiken 14:23:02 05/13/06 (8)
You need 3 distances:
Distance from speaker to side wall = a
Distance from listening position to same side wall = b
Both these distances are on lines drawn at a right angle to the wall.
Distance from line drawn between speakers to listening position = c

Mark the point on the wall level with the tweeter. The first reflection point should be
(a/a + b) multiplied by c
forward of that point.
Example:
Distance speaker to side wall = 1 metre
Distance listening position to side wall = 2.5 metres
Distance speaker plane to listener = 2 metres
Reflection point = (1/1 + 2.5) x 2 metres forward of point level with tweeter,
ie 0.57 metre forward of the point level with the tweeter.
David Aiken
- Re: First Reflection Point Formula - clio09 16:01:37 05/13/06 (6)
  Hmmm... maybe I missed something here. My measurements are as follows:
  a = 2'
  b = 6'
  c = 7'
  Using the formula:
  (a/a + b) x c gives me (2/2 + 6) x 7 for an answer of 49'. Is there an error in the formula you posted or did I screw up. I don't see how using the formula you came up with .57 metres in your example. By my math it would have been 7 metres.
  - Re: First Reflection Point Formula - David Aiken 23:01:28 05/13/06 (5)
    "(a/a + b) x c gives me (2/2 + 6) x 7"
    You read the formula as (a/a) + b which is 1 + b and that gives the answers you came up with, but that's a misread of the formula. I probably should have made it a bit clearer by writing it as follows:
    [a/(a + b)] x c
    
    so that what you're doing is dividing 2 by (2 + 6) and then multiplying that answer by 7. That gives you 0.25 X 7 or 1.75 for your dimensions.
    
    (a/a + b) is always going to be less than 1. It's a divided by a + b. You then multiply that by c and the answer will always be less than c which is great because the reflection point has to be along the wall somewhere between a point level with you and one level with the tweeter.
    
    David Aiken
    - Re: First Reflection Point Formula - clio09 09:21:12 05/14/06 (4)
      Thanks for the clarification. It all makes perfect sense now. I did run across the original site I was referring to and the formula posted there. You can follow the link to it.
      In this calculation (click on the picture) it appears the critical point is the distance from the listening position to the side wall. Once the result is derived from the formula the point is moved forward from this position, not from the speaker to wall position as in your formula. In your formula the distance is 1.75 from the speaker to wall point, here I get 1.62 from the listening position to wall point. They end up being two different locations. Do you have any thoughts on this?
      Formula (Open in New Window)
      - Re: First Reflection Point Formula - David Aiken 14:07:10 05/14/06 (3)
        
        In Reply to: Re: First Reflection Point Formula posted by clio09 on May 14, 2006 at 09:21:12:
        
        I haven't seen that formula before.
        The big difference between results is that Ethan's formula calculates a position along the wall from a point level with the listener. Mine calculates along the wall from a point level with the speaker.
        Both formulas give the same point on the wall. Mine will give you 1.25 ft forward of the speaker plane using Ethan's example. His formula gives you 3.75 feet forward of the plane of the listening position. The distance between the 2 planes is 5 feet, which is 1.25' plus 3.75'.
        So both formulae give you the identical point. Choose whichever is easier for you.
        David Aiken
        
        What am I saying?� - David Aiken 15:04:14 05/14/06 (0)
        
        In Reply to: Re: First Reflection Point Formula posted by David Aiken on May 14, 2006 at 14:07:10:
        
        I have seen that formula before.
        It's actually exactly the same formula as mine. Ethan has merely changed the location of my "c" (his Y) and transposed my "a" and "b" (his X1 and X2) at one point so that it's calculating from the plane of the listening position instead of the speaker plane. The calculation process in both cases is exactly the same.
        I'm slow this morning.
        David Aiken
        
        Re: First Reflection Point Formula - clio09 14:21:59 05/14/06 (1)
        
        In Reply to: Re: First Reflection Point Formula posted by David Aiken on May 14, 2006 at 14:07:10:
        
        I went ahead and used your formula. I was able to add an absorber panel for the right channel speaker. The refelction point for the left channel is in the middle of an archway that leads into the next room. So either I will have to mount the panel on a stand and place it in the archway or leave it as is. In any event thanks for your help.
        
        Re: First Reflection Point Formula - David Aiken 14:44:36 05/14/06 (0)
        
        In Reply to: Re: First Reflection Point Formula posted by clio09 on May 14, 2006 at 14:21:59:
        
        If the reflection point is in the middle of an archway, there's no reflection there so theoretically there's no need to use a panel at that point. The sound passes through the archway and doesn't get reflected till it hits the next wall. You could calculate the point on that wall but unless that wall is very close to the archway (say only a hallway on the other side of the arch), the wall of your room is going to block that reflection for you.
        Archways can be a little tricky, however, and you do have reflections from the room on the other side that will be difracted around the edges of the archway as they re-enter your room. You may find that placing a free standing panel so it covers the edge of the archway, overlapping a bit into the archway itself and covering a bit of the adjacent wall as well, may help things a bit. I think only experimenting will tell you whether or not you'll get some advantage.
        I have an archway beside my right speaker. The reflection point isn't in the archway but on the wall towards me. I find that covering the edge of the archway with the panel helps a bit in my room, but the geometries are different to your room and it's possible that I'm actually getting a bit of reflection from the wall on the other side of the hallway as well as the reflection from the wall inside the room. I haven't tried calculating a reflection point for the hall wall, but ensuring the panel covers about a foot of the archway certainly does help a bit.
        If you note in Ethan's diagram, he places the reflection point around the middle of the panel and when I do that with my reflection point, my panel just covers a little of the archway. I experimented a little with moving the panel sideways in both directions and discovered that moving it fractionally towards the speaker so that it covered a bit more of the archway was better. Actually, if the panel is spaced out a bit from the wall as mine are, the point at which the reflection path meets the panel will be a bit closer towards the speaker than the reflection point on the wall is, so what I've done is just centred the panel on the reflection path a bit more.
        If you're using panels on both sides, don't have them exactly opposite each other. Move one a couple of inches or so towards the speaker and the other a couple of inches towards you. You'll get a bit more benefit from doing that than having them exactly opposite each other. Varying height an inch or 2 should also help a little bit if you can.
        David Aiken
- Re: First Reflection Point Formula - clio09 15:35:04 05/13/06 (0)
  Thank you. I will give this a go.

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