Yes indeed there is. (Per my rudimentary understanding)
The impact force from a rigid hammer is like a like a spike over a few milli-seconds. From a softer hammer, the impact force is less but spread over a time.
But what is more interesting is if you take a Fourier transform of the force (acceleration), you see that the rigid hammer produces a flat response over all frequencies But the softer hammer has the peak around a lower frequency and it decays for higher frequency.
So for the wedge example : maybe it starts resonating at a higher frequency and is pushed out.
Chronos also pointed out the heat in soft media. This is a real problem when they are driving piles into the earth or ocean floor (essentially a big hammer) And they have a soft cushioning material.
I have incomplete knowledge gleamed from civil engineers doing the pile designs. I think a civil engineer will probably give you a better answer.
I don’t think so; it certainly isn’t true in my case of splitting wood because I find I can actually get a deeper split with less developed force using a dead-blow hammer, whereas with the solid sledge I’m usually hitting it with everything I have to ensure the wedge doesn’t pop out. I did start using a dead-blow because when I’m using that and a wedge or friend, I’m often trying to free a maul that has gotten stuck in a knotty or resinous piece of wood by splitting it on the opposite side and I’m concerned about the maul springing out and flailing in a random direction. With a dead-blow, even if the first hit doesn’t split the round the maul often just falls out or becomes loose enough to pull out with little force.
Since this is a shock event you actually want to calculate the shock response spectrum (SRS) or the pseudovelocity shock spectrum (PVSS) (you can actually calculate one from the other, they’re just different ways of visualizing and interpreting the shock response). You are essentially correct that as measured on the hammer a solid head hammer is going to have a broad plateau on the PVSS across a wide frequency band where a soft/shot-filled head will attenuate dramatically at medium and high frequencies because of damping.
Although in basic physics and mechanics texts an impulse is often characterized as a single impulse and resulting equivalent force, in reality every mechanical impulse or vibration into a solid elastic medium results in an oscillatory response where the vibrations tend to drive the resonances of the system, and a sharp shock essentially excites all resonances simultaneously, so you get amplification of those resonant frequencies. In the case of a steel-on-steel hammer, the response is an acoustic (or pressure) wave within the wedge that returns back to the striking hammer very quickly (speed of sound in steel is almost 6000 m/s) with most of the input energy kicking it away or transmitting into the head, whereas with a dead-blow hammer the low frequency energy spectrum is just absorbed by the dead-blow and the high frequency bounces back through the wedge repeatedly because it will have low transmissibility to the head.