For simplicity's sake, let's treat the blade as a cantilever beam, and assume cladding is perfectly welded.
The natural (resonant) frequency of a cantilever beam is going to be affected by the steel used (modulus of elasticity and density) and the geometry of the blade (thickness, height, length). The natural frequency will be proportional to:
the square root of
( (Modulus of Elasticity) x (Thickness of blade) x (Height of blade CUBED) )
( (Mass) x (Length of blade CUBED) )
The modulus of elasticity doesn't vary that much between steels, regardless of heat treat. Say in the range of 10%, which only will affect the natural frequency by about 5%. Mass also doesn't vary much with different steels, and is also a linear component of the equation.
Changes in height and length have more drastic effects because they are multiplied on top of themselves. Change the height or length of the blade by 10%, and your natural frequency is going to change on the order of 13-15%.
Since blades are thin relative to their height and length, a "small" change can actually be a fairly large change on a percentage basis. Go from a 1 mm blade to a 2 mm blade, and you've increased your resonant frequency by around 40%.
While there may be some damping due to material differences, geometry has a more significant effect on the dynamic response of the blade. Unless you're comparing blades that are exactly the same, you're looking at apples and oranges.
That said, if you don't have good physical connection between your layers, you've built a low-pass filter. If I remember correctly, a good bolted connection is only good for transmitting frequencies up to about 400 Hz--well within the audible range, as well as something that can be felt. Welds with voids will filter out higher frequencies in a similar manner to bolted connections--not at the same frequency, but they'll behave similarly--making something sound dead when you hit it with a hammer.