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RE: Clarifications on Time Coherence

Hi Villa,

I appreciate that you think I am wrong. but I am not backing away from anything.

Let us look one more time at that same vector example-- in which the upper vector was rotated by 180 degrees, to be pointing at a 225-degree angle (45 + 180), and the other remains at 315 degrees-- just as you also wrote.

Now, you and I agree they are still in quadrature, which means there is still 90 degrees between them (315 - 225 = 90 degrees).

And let each have an amplitude of 0.707, compared to having a value of One (which would be 'full output'). For the benefit of others, when each vector is drawn .707 units long, that is each driver "being -3dB at this crossover frequency".

When these two vectors are added, the resultant vector points straight down with full magnitude.
And you agree.

However, if 'cancellation' was occurring, the magnitude of that resultant vector would be Zero- it would not point anywhere-- it would not exist on the graph, as it would have a length of Zero, which is a 'point'.

But the magnitude of the resultant vector is ONE, which demonstrates how there will be NO cancellation in output when the tweeter is reversed in polarity from the woofer or vice versa, on a first-order type of speaker. Acoustic tests here confirm this.

Vector addition applets show this:
http://comp.uark.edu/~jgeabana/java/VectorCalc.html
Draw one vector at 225 degrees (into the lower left quadrant).
Draw the other vector at 315 degrees (into the fourth or lower right quadrant). Click 'add'.

On to your other point, to clarify about what happens when the phase difference between woofer and tweeter remains a constant 90 degrees-- this leads to the group delay remaining constant.

With higher-order crossovers, the constant phase difference of 180, 270 or even 360 degrees leads to the group delay NOT remaining constant, which was the point I wanted to originally make. Sorry for any confusion caused by not making that more clear at the beginning.

And to your last point:
Please note that first-order designs do not have beaming or cancellation problems off-axis. The math for that is based on pure sinewave tones measured at one point in space, and yet music is not pure sinewaves, nor do we listen at a single point. Therefore, while the math predicts what you wrote, the result on music is not what you claim.

By the way, that AES paper is 'outdated'? By that, you mean its math is no longer accurate? Wow.

Best regards,
Roy

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