I know that it quiets down the exhaust noise from a car /truck but does anyone know the scientifical aspect of what it does.
i know a bit about sound attenuation and how the sound waves are muted in the muffler and if you car is still too loud you can install a resonator but i want to know the science behind it
anyone with a background or career in this field ?

Have you tried doing some online research to see what you could find? Some exhaust manufatcurer must have a explination somewhere.

The 10,000 foot answer is that a resonator is baffled so that the reflected sound/pressure wave is out of phase with the incoming exhaust pulse. The resonator's port sizes, resonator length, and baffle placement (fiberglass has similar affect to baffles) determine which frequencies and to what extent they are attenuated.

the noise cancelling headphones work by generating a signal that has the same frequency and amplitude of the noise but is 180 degrees out of phase.

I know, I know!! It resonates!!!!!!!

...A previous post on this similar topic.

https://board.moparts.org/ubbthreads/showflat.php?Number=5262371

The resonator is basically a
"big change"
that the sound wave encounters on its journey down the exhaust.

When the sound wave comes down the small exhaust pipe and enters the larger pipe diameter of the resonator,
the abrupt change in area causes a reflected wave backwards towards the engine.

If you need to have a picture of this in your
'Mind's Eye',
this is like the waves in rapids of a river suddenly entering a large lake.
It is the opposite situation to an ocean wave hitting the small entrance to a bay.
In both situations waves are reflected.

In a practical sense, a resonator in effect breaks up the length of the small exhaust pipe into smaller lengths.

If you have length of exhaust pipe between 55 and 75 inches, you would do well to put a resonator in the middle.

Exhaust pipes 'resonate' at different musical notes, just like the long flutes with holes to vary the length,
and the big Pipe Organs in old churches.

The same thing happens if you blow cross ways on the opening of a beer bottle.

If you have an annoying 'drone' noise at some RPM and throttle opening,
you can get rid of it by putting a resonator somewhere in the middle of the length of exhaust pipe, which will turn the 'bad' low frequency drone into two high frequency noises that are not as annoying.

At certain RPMs and throttle settings,
the reflected pulse of sound from the resonator can actually 'cancel' out another noise.

This is the same 'anti-noise' science that high-$ Bose noise reducing headphones use.

With a simple resonator it only works in a narrow sound range though,
although careful design can make the best of it.

The science of this is covered with fancy math at this
General Motors Kettering Institute for Engineering and Management
self-learning course for automotive engineers:

http://paws.kettering.edu/~drussell/GMI-Acoustics/Filters.html

The science of a
Pipe Organ's music
and the noise from an engine exhaust
are closely linked.

You could actually experiment with stuff like this in your bath tub with boards to make different width channels, and use your hand to make waves in the water.

Don't laugh,
this is very similar to what our class did in the laboratory 'wave table' in the PSSC version of High School Physics in 1973.

Sadly, kids today don't get this kind of 'hands-on' High School Physics training.
PSSC Physics came about after the
"1957 Sputnik Scare"
that the Russians were pulling ahead of the USA in Science,
so an serious attempt was made to really teach Physics well to high school students.

http://www.compadre.org/portal/pssc/docs/Haber-Schaim.pdf

360view, not laughing at all exp as that was a very good exp. I want to break the 29 MPH that Dave did w his 318 Barracuda & I think the right pri dia/length is pretty important & 1&1/2" pri was suggested though it'd be a custom deal as afaik only the Hooker 1&5/8 supercomps are offered in an equal length and on the 451 65 dart if I go w 3" mandrel it's gonna take an X pipe/Dynamax hemi length super turbo muffs/resonators and a bit of science to keep it quiet enough to suit me and if I cant then some cable operated cutouts which actually now that I think about it is a far better way to go as when I'm ready to take someones money I can pull 2 cables & be ready and have peace and quiet the rest of the time plus the quietness will not scare them and make them more disposed to wager a higher amt .

If you were into fabricating you could make your own headers or you can get the smallest diameter ones you can find and saw off the collector and add longer tubes in and then attach the collector farther back. That is one thing I had that was just not ideal on my car but I think you will get bigger gains from gearing it higher and the induction side of things, probably little difference on the ex side as long as it is close

If it is higher MPG that you are after,
my suggestion would be:

Spend money on just the right gearing to get the throttle about 80% open at the engine rpm you are travelling at.

Spend money on aerodynamic improvements if your travel is above 40 mph.

Spend money on tires that have the lowest rolling resistance possible, with the level of safety for braking and cornering you are willing to live with.

Spend money on higher compression pistons and cylinder heads.

All of the above are likely to give
"More Bang for the Buck"
than exhaust system modifications
to improve MPG.

If you are insistent on playing with the exhaust system, then your number one priority should be:

"What is my exhaust back-pressure at different RPMS and throttle openings now?"

Buy a pressure gauge that can read 0-10 PSI and connect it to your exhaust manifold outlet with enough steel brake line to let the gas cool down and not damage the pressure gauge.

I think you are going to find that in daily driving at part-throttle the exhaust back-pressure is already low, probably less than 2 psi.

When the engine is not at
full throttle at 4000 RPM
there is just not much exhaust gas to begin with,
and reducing its pressure may improve MPG,
but the amount is tiny.

Are you willing to spend hundreds of $
to gain 0.2 MPG ?

Spend that money on tires and you might get
2 MPG.

To really do the engineering on the exhaust
you would actually need a recording oscilloscope and both a very fast acting pressure sensor,
and a camshaft position sensor,
the o'scope could read.
You would use this high $ combo to make the reflected low pressure pulses show up at your exhaust valve seat inside the right 'time window' for the rising piston to benefit from.

How to do this on the cheap with special headers?

Maybe convince a student at UNC-Charlotte
in their NASCAR engine mechanic program
to do it as his/her senior project,
with David Vizard overseeing it.
It would be a great 'demo' project to have on a Resume that would probably get that student a job with an exhaust products company.