**Answer:**

6) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction.

**Explanation:**

What matters is the part , the other parts of the equation don't affect time and space variations. We know that when the sign is - the wave propagates to the positive direction while when the sign is + the wave propagates to the negative direction, but <em>here is an explanation</em> of this:

For both cases, + and -, after a certain time (), the displacement <em>y</em> of the wave will be determined by the term. For simplicity, if we imagine we are looking at the origin (x=0), this will be simply .

To know which side, right or left of the origin, would go through the origin after a time (and thus know the direction of propagation) we have to see how we can achieve **that same displacement **<em>y</em> not by a time variation but by a space variation (we would be looking where in space is what we would have in the future in time). The term would be then , which at the origin is . This would mean that, when the original equation has , we must have that for to be equal to , and when the original equation has , we must have that for to be equal to

<em>Note that their values don't matter, although they are a very small variation (we have to be careful since all this is inside a sin function), what matters is if they are positive or negative and as such what is possible or not .</em>

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In conclusion, when , the part of the wave on the positive side () is the one that will go through the origin, so the wave is going in the negative direction, and viceversa.