ORIGINAL: jpkeys
Signal level is NOT volume. Volume is more closely associated with power, as in the "constant power" pan laws. Volume is the combination of what you hear coming out of two speakers.
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Great explanation...sometimes the details of working with audio are not that obvious (...and semantics can be a b**** as well)
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As for the sin/cos vs square root panning thing...they are just 2 types of functions when processed correctly add up to a constant value.

The sample values that get recorded are voltages and power is proportional to the square of the voltage. Also, it's convenient that:
1. sin^2 (x) + cos^2(x) = 1 and
2. x + (1-x) = 1

To maintain constant power we just need to multiply each side (L/R) by the appropriate square root of each term, ie. sin(x) and cos(x) OR sqrt(x) and sqrt(1-x). Let the voltage be y and x be the panning amount. Since the total power equals the L power + R power and power is proportional to voltage squared we have either:

1. L: y*sin(x) R: y*cos(x)
2. L: y*sqrt(x) R: y*sqrt(1-x)

For total power we square each term and add together:
1. y^2*sin^2(x)+y^2*cos^2(x) = y^2*(sin^2(x)+cos^2(x)) = y^2
2. y^2*(sqrt(x))^2+y^2*((sqrt(1-x))^2) = y^2*(x+(1-x)) = y^2

From these equations we see that for any input and any panning amount we achieve a constant power output (and that correlates roughly to equal volume).

The graph of sin/cos and square root of x look like this. There's not much info to glean from this other than they are 2 different options that obtain the same goal...(click image for full view):


Here was another taper visualization that might seem more intuitive...yellow is sin/cos and red is sqrt...
taper-sin-sqrt.jpg

Thanks a lot!

There are some really good panlaw descriptions here. The confusion seems centered on apparent volume vs. signal level/str. Hopefully that difference has registered, otherwise panlaw is always going to be mirky business. Bottom line, you generally want to manipulate your real volumes -- signal level be damned. Level, re pan, is only useful in so far as it manages intent, unless you're trying to match some old mixing deck. So fuggetaboutit.

But here is the real world situation that might also help bring it home: your mix is almost perfect, and the only thing you now wanna do is just move one little guitar a farther left in your stereo field.

So you rotate left and either
. ...a) it suddenly also decreases in volume (0dB const) or
. ...b) the levels happily stays the same (-3dB).

(For extra credit, what might be the consequence to master bus level, if you left no headroom going into this?

--Joe "Just leave it at -3dB unless you have a good reason to change it" Tabby

Great Stuff Thanks Everyone ,very helpfull

taccess
Great Stuff Thanks Everyone ,very helpfull

If nothing has changed with the pan laws since Sonar 6, then this post has very useful information.
 

Here's an article I wrote called The Truth about Panning Laws.
There's also a shorter SONAR-specific blog post on this site - Five Questions about Panning Laws.

Hey, Craig, I just noticed that your bio blurb says you've lectured in three languages. This is a side of you that I was not aware of. Are you actually fluent in three languages? I assume that living in the Southwest, one of those is Spanish. What's the other?

I'm fluent in English and French, and have given seminars in Spanish. I wouldn't consider myself fluent in Spanish, but I know enough to give presentations (and I also know crucially important phrases like "dos mas cervezas, por favor" ). 
 
True story: I was giving a seminar on synthesis in Argentina, and referred to adding vibrato with the "rueda de modulacion." People looked at me with total confusion...some asked what the "rueda de modulacion" is, and I said it's the controller on the left side of the keyboard. "Ah, si, si! Yo comprendo...el mod wheel!" Seems they just called it a mod wheel. Like French people saying "weekend" or us saying "joie de vivre."

papa2004
You might be surprised at how often users fail to consider using a search engine to find the simplest of answers...The number probably resembles the same percentage as those who never consider using the Help files or consulting their manuals...

 
I just Google'd that. It's 78%...
 
Walt
 
PS: Did you know that Google should have been spelled Googol or 1e+100 !

I'm more jealous about the 3 languages than your tech chops Craig. I wanted to learn another language and always failed. Too lazy or just not wired for it, I'll never know.