but seeing how complicated things can be, I decided to slightly rewrite the scene.

However, I'm glad that you were willing to step up to the challenge.

Rule 1 of this battle: Write what is funny or otherwise advances your story

But for a scientific background:

As hS has mentioned, waves in a solid medium can be of three types (well actually more than three but for real earthquakes there's the three he's mentioned), all of which can exhibit interference. Technically, none of these is a true shock wave (which is basically a near-instantaneous change in the properties of a fluid and is non-linear). A linear wave, such as most we encounter in daily life, can be modelled using the principle of superposition- ie the effect of mixing the two waves is the (vector) summation of the two waves, with the magnitude, frequency and phase of the wave determining the sum.

I'm not up to speed with Pokemon, so unsure whether these powers are a single pulse of energy or whether it's something more persistent.

If it's pulses, their frequency content is broadband (they don't have a characteristic frequency) and only the magnitude and length of pulse matters. Depending on where you are on the waveform you'd get firstly reinforcement where the positive parts add, then (if the pulses are different duration) destructive interference, then finally (negative) reinforcement. In general terms where the pulses meet you end up with the two powers most likely combining unless one power is a slower, more spread-out burst of energy in which case the magnitude would be lower.

If they're waves (ie repeating waveforms) they will interfere, either constructively (171%) or destructively (29%) depending on where within the cycle the waves are when they meet. The effect will be a spatially-varying waveform so the damage will range from 29-171 if the combatants move slightly.

All this assumes that the waves are pure waveforms in coherent phase so that interference can occur. This is actually pretty rare in real life - more often "real" waves are in random phase relationships and add incoherently, which is just adding the energy of the waveforms together (energy is proportional to the amplitude squared so any positive or negative amplitude differences don't cancel when adding energy. Adding energetically results in the combined waveform being (on average) 122%.

Tl;dr version: you're most likely to get spatial/temporal variations in the damage from 29% to 171% as the combatants move and fire their powers at different times. As a story mechanic this could be interesting by basically including a randomised "critical hit" variability to the damage. It would be difficult/impossible to time the powers so that damage I'd always minimised/maximised.

Elcalion, acoustic engineer by day

in a shockwave, one particle is thrown forward by the force and hits another particle, which is also thrown forwards. when two particles hit each other, they will push each other in different directions, like a reverse tug of war. cancel out, I think. in real earthquakes, when two earthquakes collide, this is what happens: one cancels out the other. however, where they meet, the land is jolted about more than usual.

I’m not sure whether this should be a physics question. Isn’t what it canonically looks like in-game more important than how it would work in real life?

Unfortunately I never paid much attention when my daughter played Pokémon, so I don’t know whether an attack may be partially canceled out by a similar attack.

(More unfortunately, I’ve once been a nuclear physicist, but I have no clue to this geophysical question, so I’m just trying to avoid an answer.)

HG

The way I'm arriving at that answer is by considering the other two options. 'Earth-waves' are like sound waves, in that they're longitudinal - at least, I hope so! I suppose they could be transverse... anyway. That means they can interfere either constructively or destructively - a 171% outcome or a 29% outcome.

Now, in the pass-through option, either makes sense. You either get a massive peak in the middle, or a deceptive low zone. No problem there.

But what about the other option? If they destructively interfere, you'd get zero Magnitude and 29% Earthquake. But if they constructively interfere? Your description would have the Earthquake coming out at 171%, and the Magnitude vanishing. In effect, you'd be asking the Earthquake to reflect the Magnitude, which... doesn't seem plausible.

Another way of looking at it: if they are longitudinal waves, then they are sound waves - just through a solid, not a liquid.

~

Further checking reveals that earthquakes actually feature three sorts of waves: longitudinal P-waves, transverse S-waves, and surface waves, ie ripples. The P-waves travel roughly twice as fast as the S-waves, but those are still km/s measurements - for your purposes, they're instantaneous. Still, as far as I'm aware, transverse waves exhibit the same interference patterns as longitudinal. If you're really interested in showing minutae, you could have one set cancel, the other magnify, so the earth stops trembling but suddenly jolts massively up and down.

And of course, as I said, this is instantaneous. So they 'meet' everywhere between the two Pokemon, and indeed all around them. This does suggest you could use a well-tuned Magnitude to protect you from the effects of Earthquake... or maybe the waves just propagate slower there. Though they shouldn't.

hS