IB Physics help

hey guys, Im going through past exam questions that my (awful) teacher gave me and I'm confused. It says: outline what is meant by the principle of superposition of waves. (2 marks) I kind of remembered but wasnt sure so checked my textbook and finally wrote: the principle of superposition of waves is when 2 waves of equal frequency and amplitude travel at the same speed towards each other and meet, and cancel each other out and form nothing. Here's what the mark scheme says: when 2 waves meet the resultant displacement
is the «vector» sum of their individual displacementsDisplacement should be mentioned at least once in MP 1 or 2.It's so unclear, I'm so confused. WOuld i have gotten 1 mark? what's resultant displacement? what does displacement have to do with anything? what's a vector sum?

Please help, my physics exam is tomorrow morning and i'm not ready!!!???!

So your definition is an example of what could happen, due to the superposition of waves. In your case, the waves meeting would be completely out of phase, meaning the crest of one wave would meet the trough of the other, and vice versa. This means they would cancel each other out, or destructively interfere.

The mark scheme's definition of the principal of superposition is a good one, so the resultant displacement is the vector sum of each individual displacement. What it means when it's talking about displacement is how far away from the undisturbed position (the centre line) any point on the wave is. So at the crest, the displacement (from the undisturbed position) will be the greatest, which is the amplitude. And at the trough, the bottom point, the displacement will be the lowest. These will be the same in terms of distance, but in terms of displacement, where direction is considered, they are opposites. So if you consider the displacement at the crest to be x, then the displacement at the trough will be -x. If these meet, they are going to add to the resultant displacement. In this case, it will be x + (-x) = 0, so they will destructively interfere. If 2 crests were to meet, if the waves meet in phase, the resultant displacement would be x + x = 2x, which is double the amplitude, so the intensity doubles. This is constructive interference.

So with numerical values, if 2 waves met, and one wave, at a certain point, had a displacement of 5mm, and the other had a displacement of 10mm, the resultant displacement will be 15mm at that point. And that's what's meant by vector sum, the directions are considered as well as magnitudes.

On the image I've attached, a) would be constructive interference and b) would be destructive interference.

Hope this helps clear it up, good luck for your exam.

OMG THANK YOU SO MUCH.
one more question though, so by displacement you mean like the amplitude? so like if the amplitude is 5mm of one wave and 15mm of the other, it's constructive interference and they superpose so they make up one wave of amplitude 15mm? or not?

Well the amplitude is the maximum displacement from the undisturbed position. So on a wave, the crest's displacement will be the amplitude, but other points on the wave, for example, half way up the curve (to the crest) will not be the amplitude. In this case, half way up the wave would be half way to the amplitude, so the displacement would be the amplitude/2. If you were given values on the y-axis of the graph for the wave, then the y-value at any point would be its displacement. But you might not even need to consider displacement numerically, so if it still confuses you I wouldn't worry too much about it.