An very old piece of valve technology that might be useable in pulse jets is
the double reed valve!
For those of you who have not dismised the idea out of hand, and are still reading this, the double read valve is what makes the noise in a bagpipe.
It has one very big flaw for use in a pulse jet?
And two equally big advantages!
Firstly the valves would mounted on the up stream / cold side of the valve plate, well away from the hot gasses.
Second the valves 'role' closed rather than slamming shut.
Third (I said two big advantages, there are also some minor ones.) in the open condition the air as a straighter path through the jet.
Fourth it tends to favour the production of the odd harmonics, hence the nasal sound of the oboe.
The disadvantage is it faces the wrong way.
All is not lost “we can rebuild it. We have the technology”.
But first a digression.
Take a broad thin walled drinking straw, and cut about 2 or 3 inches of it. squash half of this short tube flat, then cut of the two corners that you have made. That is a simple double read.
\_/ Unfortunately the rebuild is not minor.
You could try to use a tuned inlet like they use on valveless pulse jets to create a high pressure wave out side of the vales at the same time as there is maximum pressure inside. I wish I could tell you how that is done, but I need some one to tell me first?
The alternative involves tuning the exhaust pipe into a half wave oscillator, when it naturally wants to be a quarter oscillatory.
This trick is managed in one of two ways.
first by fixing a pressure node just behind the valve plate.
And this trick is accomplished by drilling large holes through the side of the tube just behind the valve plate
(very drastic and irrecoverable ) so that the air pressure behind the valve plate stays the same as the out side air. Then fitting over those holes a set of closed resonance tubes of a quarter of a wave length of the new, higher pitched, shorter wave length of the tube. About half the physical length of the tube. (this is only an approximation, in practice these lengths might be a bit shorter, some trile and error will be called for. (do you really want to be even thinking about doing this with your pride and joy )).second by creating a pressure anti-node.
A second set of holes connected to closed tubes of a bout half way down the exhaust pipe, these tubes would have to be half a wave length long ( as long as the exhaust pipe its self 
), and in a proper jet would probably have to be wound a round the exhaust to stop them sticking out of the back. This arrangement as the added advantage of injecting hot exhaust gasses back into the jet at the time and place of maximum pressure.
With on gas pressure acting upon them, what will make the valves work,
SOUND. The same thing makes the double read open and close no a bassoon.
This is where I loose the interest of that last fraction of a percent those of you that have stuck with this so far.
Unfortunately the maximum sound pressure dose not coincide with maximum gas pressure and I suspect that this will under mine this design.
Still you've read this far because the advantages of the double read valve are worth that much effort. Now I think it is worth the effort of a some more knowledgeable than me to come up with a workable solution.
