Does the resulting wave demonstrate destructive interference? explain your answer.

Destructive interference happens when one wave is oscillating the opposite way as the other one, so it compensates.

For example:

Let’s say one wave can be described with this formula:

f(x)=sinx

And the other one, with this formula:

g(x)=-sinx

So when you add them, you get 0 for any x value:

h(s)=f(x)+g(x)=sinx-sinx=0

(I recommend to put them in a graph software such as GeoGebra, to see how they look like).

In other cases, the sum of both can be bigger than each one of them. That is called constructive interference. For example:

Wave 1: f(x)=sinx

Wave 2: g(x)=2sinx

Total: h(x)=f(x)+g(x)=sinx+2sinx=3sinx

which is bigger than sinx, and also higher to 2sinx, for any x value.

If you have the graph instead of the formula, take 2 points from the graph which have the same x value, one in the first wave and the other one in the second wave, and add them (y1+y2). If both numbers are the same but one is negative and the other one is positive, the sum will be 0, and that is a destructive interference.