<span>anything harder than mohs scale 7 so eg Topaz, Corundum and diamond representing mohs scale 8 9 and 10 respectively.</span>
The work-energy theorem states that the change in kinetic energy of the particle is equal to the work done on the particle:

The work done on the particle is the integral of the force on dx:

So, this corresponds to the change in kinetic energy of the particle.
When crest of one wave interferes with the trough of other wave, the amplitude of the resultant wave formed is less. Hence the type of interference is destructive interference.