So as a follow-up on the cardioid SUB files i posted some time ago **https://timobeckmangeluid.wordpress.com/2011/11/08/end-fired-sub-array-only-in-english/**

**https://timobeckmangeluid.wordpress.com/2011/11/18/why-even-bother/**

There are a few things i did not post about and among them is the difference between subs in a conventional Left & Right set-up and subs in a line . So here we go………

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First lets look at the conventional LFT/RGHT set-up . Again I’ll be using the MAP on LINE program from Meyer sound and the RBV2-9 Phase calculator witch visualizes the phase response from individual loudspeakers by importing the impulse response from the MAP program .

**So in order to understand the following you have to know what happens if you have 2 or more sources that have phase differences .**

**Also it helps to have the following list present @ all time .**

**0° 0 wavelength – 360° 1 wavelength – 720° 2 wavelength – 1080° 3 wavelength = max 6db addition (if level matches) . **

**120° 1/3 wavelength – 480° 1 1/3 wavelength – 840° 2 1/3 wavelength – 1200° 3 1/3 wavelength = 0db addition . **

**180° 1/2 wavelength – 540° 1 1/2 wavelength – 900° 2 1/2 wavelength – 1260° 3 1/2 wavelength = max cancelation .**

**240° 2/3 wavelength – 600****° 1 2/3 wavelength – ****960° 2 2/3 wavelength – ****1320° 3 2/3 wavelength = 0db addition .**

I have drawn a “centre line” and placed the mic @ 15mt on-axis . So @ this position there are very few phase problems because all subs arrive approximately at the same point in time at the mic position . So if you look at the phase response at the mic position you get the following .

On the left you see the solo responses of the left and right stack and on the right the sum of both stacks . No comb filters @ this mic position so maybe no problems ? To bad . In the first screenshot of this post there are marks . These marks are also @ 15mt distance but are of axis (15° per mark) . Now let’s take a look what happens if i move the mic .

Mic position @ 15mt. 15° off axis :

@ 93Hz cancelation a bit of addition @ about 45-50Hz

Mic position @ 15mt. 30° off axis :

@ 47 & 143Hz cancelation and addition @ 80Hz

Mic position @ 15mt. 45° off axis :

@102 cancelation and addition @ 69Hz

Mic position @15mt. 60° off axis :

@ 82Hz cancelation and addition @ 55 & 98Hz

Mic position @15mt. 75°off axis :

@ 75Hz & 125Hz cancelation and addition @ 49Hz & 92Hz

Mic position @15mt. 90° off-axis :

@ 72Hz & 122Hz cancelation and addition @ 40-50Hz & 85Hz

So you can see that although there are no problems in the on-axis position the other mic positions show a lot of comb-filtering . Because i moved the mic to the left stack it’s level is higher than the right stack and because of this the level doesn’t drop to –infinity but still the cancels will be clearly audible .

The problem you have working with analyzers is that you are looking @ 1 position @ all frequencies at the time (the 1/4” of space of the mic capsule) . It would be nice if you could see the whole room but to bad you are looking through a microscope at the 1 point you put the mic at all frequencies .

So if you start to work with MAP on Line (or any other prediction program) you can look at the whole room but just at 1 frequency at the time . So lets take a look at 1 position the 45° position for instance .

Mic position @ 15mt. 45°** **off-axis .

So the RBV program gives a addition in the 60-70Hz range and a cancel at the 100Hz area . In order to find the exact frequencies i had to take the map prediction because of the frequency scaling within RBV .

So now lets take a look at the room prediction from Map at the 2 frequencies that show “problems” at the 45° off-axis position in this case 69Hz and 102Hz .

**MAP ON LINE @ 69Hz @ 15mt. @ 45° off-axis**

**MAP ON LINE @ 102Hz @ 15mt. @ 45° off-axis**

I have prepared a PowerPoint where you can see the room @ every frequency from 39Hz up to 125Hz .

**PowerPoint** (press “diavoorstelling starten”)

So although this set-up is one of the most used from the start of professional sound reinforcement up to the present and probably in the future it has a lot of cancel and addition areas in the frequency response all over the room . All of the cancels and additions are due to phase and level differences between left and right at all positions in the room (except the on axis position) .

So if you looked at the PowerPoint in the second part there was a **sub-line** set-up . And here is the start

Again I’m going to take a look at the solo response of every sub at every mic position and the combined response of all 4 at every mic position .

**As a little reminder : here is the list again .**

**0° 0 wavelength – 360° 1 wavelength – 720° 2 wavelength – 1080° 3 wavelength = max 6db addition (if level matches) . **

**120° 1/3 wavelength – 480° 1 1/3 wavelength – 840° 2 1/3 wavelength – 1200° 3 1/3 wavelength = 0db addition . **

**180° 1/2 wavelength – 540° 1 1/2 wavelength – 900° 2 1/2 wavelength – 1260° 3 1/2 wavelength = max cancelation .**

**240° 2/3 wavelength – 600****° 1 2/3 wavelength – ****960° 2 2/3 wavelength – ****1320° 3 2/3 wavelength = 0db addition .**

So first the on-axis position . On all 4 subs the relative distance to the mic is about the same so the time/phase difference is minimal so again This set-up will have addition there .

(Looks like it’s only 2 subs but at the right you can see a level addition of 12db . If it where only 2 subs the addition would be 6db) . Next is the :

**15° off-axis position :**

At this mic position there is still a lot of addition but @ +/- 80Hz there’s level reduction up to 230Hz .

So let’s look at what is happening here . On the left you have the solo responses of S1 to S4 . The **SUM** of all traces combined **BLACK** can be seen in the right screen . This set-up will have addition up to about 125Hz @ the 15° off-axis position @15mt. distance .

The blue trace (S1) and red (S2) are about 30° out off phase from 110Hz and the phase difference increases to about 60° going higher up the frequency scale . They also have a minimal level difference of 0,2db . So they will have a addition ranging from 5,62db to 4,67db .

The blue trace (S1) and green trace (S3) are about 30° out off phase from 40Hz and the phase difference increases to about 120° going higher up the frequency scale to 125Hz and a level difference 0,6db . So they will have a addition ranging from 5,43db to 0db @ 125Hz (cancelation starts here between S1 & S3) .

The blue trace (S1) and orange trace (S4) are about 60° out off phase from 40Hz and the phase difference increases to about 120° going higher up the frequency scale to 80Hz and a level difference 0,6db . So they will have a addition ranging from 5,43db to 0db @ 80Hz (cancelation starts here between S1 & S4) . Maximum cancel is @ 110Hz between S1 & S4 .

The red trace (S2) and green trace (S3) are about 30° out off phase from 63Hz and the phase difference increases to about 120° going higher up the frequency scale to 200Hz and a level difference 0,4db . So they will have a addition ranging from 5,52db to 0db @ 200Hz (cancelation starts here between S2 & S3) .

The red trace (S2) and orange trace (S4) are about 45° out off phase from 40Hz and the phase difference increases to about 120° going higher up the frequency scale to 90-100Hz and a level difference 1db . So they will have a addition ranging from 4,85db to 0db @ 90Hz (cancelation starts here between S2 & S4) .

The green trace (S3) and orange trace (S4) are about 30° out off phase from 40Hz and the phase difference increases to about 120° going higher up the frequency scale to 140Hz and a level difference 0,6db . So they will have a addition ranging from 5,43db to 0db @ +/-140Hz (cancelation starts here between S3 & S4) .

I’m not going to do all of the above on every mic position but it should be clear by now what’s going to happen in the rest of the mic positions . The phase and level differences between all subs at the different mic positions is going to give you more and more cancels moving in the direction to the 90° off-axis position .

**30° off-axis position :**

@ the 30° off-axis position there’s still a small addition area @ the low end up to 63Hz between S1 to S4 but after that the level of all 4 does not rise compared to just S1 solo (just a small bump @ 125Hz but that’s just a very small increase of level).

S1 and S2 have a cancel area @ 220Hz and addition up to about 140/160Hz (after that the phase difference between them exceeds 120° so there it starts to cancel in this set-up) .

S1 and S3 have a cancel area @ 95Hz and addition areas up to about 63Hz and 125Hz up to 220Hz (after that the phase difference between them exceeds 120° so there it starts to cancel in this set-up) .

S1 and S4 have cancel areas @ 56Hz and 171Hz and a addition area @ 93Hz (after that the phase difference between them exceeds 120° so there it starts to cancel in this set-up) .

S2 and S3 have a cancel area @ 171Hz and addition up to about 125Hz (after that the phase difference between them exceeds 120° so there it starts to cancel in this set-up) .

S2 and S4 have cancel areas @ 171Hz and addition areas up to about 40Hz and 125Hz (after that the phase difference between them exceeds 120° so there it starts to cancel in this set-up) .

S3 and S4 Have a cancel area 146Hz and addition up to about 90Hz (after that the phase difference between them exceeds 120° so there it starts to cancel) .

**45° off-axis position :**

So @ the 45° off-axis mic position the level of all 4 subs only adds at the really low end and around 250Hz (this is outside the normal operating range of the subs used). From about 40Hz to about 200Hz the level of all 4 subs does not rise above the level of S1 (blue) solo . This means there is still sound @ this position !!!!!

From here on I’m going to skip all of the explanations at every screen shot . You should be able to do them yourself .

S1 + S2

S1 + S3

S1 + S4

S2 + S3

S2 + S4

S3 + S4

**60° off-axis position :**

S1 + S2

S1 + S3

S1 + S4

S2 + S3

S2 + S4

S3 + S4

**75° off-axis position :**

S1 + S2

S1 + S3

S1 + S4

S2 + S3

S2 + S4

S3 + S4

**90° off-axis position :**

S1 + S2

S1 + S3

S1 + S4

S2 + S3

S2 + S4

S3 + S4

So @ the 90° off-axis position the summed level of S1 to S4 is even lower than the S1 solo level . If you take a look at the **PowerPoint** again and the frequency response of the sub-line over the entire room you can see the advantage of this set-up . On-axis addition off-axis cancelation . The coverage zone dictates the length of the sub-line and the wave-length of the upper x-over frequency x 2/3 dictates the distance between the subs centre to centre . (so if your x-over frequency is 100Hz the max distance between subs is 3,4mt(@15°C) times 2/3 = 2,26mt centre to centre).

You can reduce the distance between them and get more level due to coupling and more subs needed in the line to cover the area but never increase the distance between the subs than 2/3 of the wavelength of the upper x-over frequency of the subs . The reason for not increasing the distance can be seen past the 125Hz area going up the frequency scale . A side lobe will appear there .

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