I have learned that when two waves are combined, the peaks and troughs could be in the same direction (so that means the amplitude is increased) or the peaks and troughs could be in the opposite direction (so that means they are cancelling out each other; meaning nothing is produced)
According to definitions online, "standing waves can be produced by any two identical waves traveling in opposite directions that have the right wavelength"
Why is it that these "two waves in opposite direction" not cancel out each other and instead they create a "standing wave"?
Best Answer
They do cancel each other when the peaks of one coincide with the troughs of the other, but since they move in opposite directions, this only happens at specific moments in time (every half period). At other moments (one fourth period later), the peaks of both waves will coincide (and so will their troughs).
In the figure above, the red and green wave move in opposite directions, the blue wave is the sum of both. If the red and green wave moved in the same direction and the phase difference was 180° (meaning peaks of one coincide with troughs of the other), they would indeed cancel each other out at all times.
(image by Yuta Aoki, wikipedia commons)