Maybe this will explain it better for you;
If you need guidance sizing your headers or if you're simply having difficulties trying to find the right header size or collector form, check out what this month's tech article has to offer! We took a set of Doug's headers, tried out different collector styles and hooked it up to the dyno...
www.motortrend.com
It confirms my initial assertion that 4-stroke exhaust tuning is about the sonic pulse energy and not the inertia of the moving gas column.
But, run the maths and it doesn't really compute.
I work with the speed of the pulse as 500 m/s (1600 ft/s) which is higher than you quote but despite this my case isn't at all weakened.
Take 3000 rpm as the target rpm. Each revolution takes 0.02s, 180 CAD (crank angle degrees) takes half that (0.01s) and using that figure gives from opening of the exhaust valve to BDC for the pulse to be established in the exhaust port. 180 CAD from there takes us to TDC and the valve overlap period - where the returning negative pulse supposedly arrives to do its work.
V = d/t where V is velocity, d is distance, t is time.
d = V x t = 1600ft/s x 0.01s = 16ft = 192''. The pulse has to traverse the primary twice so the required length of the primary is half that ie 192/2 = 96'' which is double the longest mentioned primary length of 48''.
Alternatively, we can take a 40'' primary and calculate where in the exhaust event it will arrive.
t = d/V in this case d = 2 x 40'' = 80''
t = 80''/1600ft/s = 80/(1600 x 12)''/s = 0.004s. Each revolution at 3000 rpm takes 0.02s so
(0.004/0.02) x 360 CAD = 72 CAD.
72CAD from BDC is nowhere near the valve overlap event and I've been generous in giving the pulse until BDC to be established and generous with its speed. Even calculating for 6000 rpm gives a primary length of 48'' - which is regarded as a long primary more attuned to low rpm operation.
The article mentions secondary pipe length as being crucial and perhaps/possibly that makes the difference though it is far from obvious how (unless we assume there are two returned pulses with the second one arriving at around TDC but that would imply a secondary length similar to the primary length) but the point here is that that primaries alone at the usual lengths do not return a scavenging pulse to coincide with the valve overlap period.
If any sees a flaw (or flaws!) in my calculations please correct me. But this is the methodology I apply to to 2-stroke pipes (hence my choice of slightly higher pulse speed) and it's always been accurate.