Can anyone help me understand
1) why the intake/exhaust manifold runners must have equal length?
2)How the half order noise is generated?
3)Why does half order content affect sound quality?
This is a topic for the engine forum, there is a wealth of discussion about manifolds there.
my $0.02:
1) Equal length runners are good for balanced cylinders. However, it does not gaurantee it. Flow balance and equal length runners must be developed.
2.) Half order pulses can be generated by unequal length runners. The noise is produced from interaction in the plenum or possibly from the shapes of the intake system.
3.) Sound quality is very difficult to define, but generally there are "pleasing harmonics" to the human ear. I dont know exactly how to define that, but I know half orders that have high magnitudes are not pleasing. Resonators in an intake system are sometimes required to take out half orders to increase sound quality. Generally when you have a system w/ unequal length runners.
1) they don't have to be and very rarely are on production cars
2) each cylinder is creating a firing pulse at half order. Any errors in phasing when adding them up will allow some of the original 1/2 order to be transmitted, whereas if you get it right they'll add up constructively to give one n/2 signal. try it yourself, adding up 4 sine waves that are 90 degrees out of phase with each other, then try moving one to 91 degrees etc.
3) Because multiple harmonics inside the effective bandwidth of the ear (100 Hz-1/3 octave) are heard as a muddy tone instead of a pure tone.