As you can see on this picture (FIG. 1), if you need to close a thermoacoustic standing wave engine, then the closed resonator part (right side) should be same length as left side, the sound generator base.
The whole system is a half wavelenght thermoacoustic engine.
The stack's center on the λ/8 exactly.
But what we can do with a mechanical resonator?
We can replace the whole resonator tube length( λ/4=4/8 of whole tube length) + the volume between the cold heat exchanger to the resonator tube ( λ/16= 1/8 length).
So what we can do?
We can replace the whole length 5/8th part.
That is nearly 2/3 of full length!
After we get a short engine like this:
Where the 104 is a buffer volume. This volume help for the gas flow going trough the 112 stack
also the 108-110 heat exchangers.
114 is the piston and the back side is a generator also "gas spring volume", or solid spring of course.