waves help?

Loo0k at fig 4 on this page.
http://cnx.org/content/m42508/latest/?collection=col11406/latest

At R there could be, say, 5 wavelengths of the lower wave and 4 of the upper wave in the space between the slits and R
At Q there could then be, say, 5 wavelengths of the lower in the space and 4½ of the upper.

The exact situation will depend on the setup. This isn't given in your diagram.

The oscilloscope measures the resultant amplitude of the sound wave at the point where it's placed.
When it's at a point where constructive interference occurs between the waves from the two speakers you will get a large amplitude on the trace.
When it's at a point where destructive interference occurs you will see a very small or possibly zero amplitude trace.

Therefore what occurs in the example above? When we move the microphone right, what will happen in terms of wave phenomena? It will go from constructive to destructive?

What do you think?
What happens (on a plucked string, for example) when you get two identical waves travelling in opposite directions? In the string this is caused by reflection. Here the waves are both created at either end, but the result is the same.

Hint.
Underneath my first post (or maybe even this one) there is (should be) an animation depicting this very thing.

You get destructive interference? or maybe a superposition wave?

You didn't answer my question about what you get on a vibrating stretched string.
Do you know what nodes and antinodes are?
Have you heard of standing waves?

Yes I've heard of both but according to my teacher these aren't meant to be relevant for this question. I'm still a little confused though, I take it if we move the microphone right, the oscilloscope will show a maxima and minima due to wave construction or destruction? Which one is it in maxima and minima?

My explanation involves standing waves and nodes/antinodes. In my view they are relevant. There's an antinode at the mid point. You had better ask your teacher for his/her explanation. I'm afraid I have to disagree.
If there is an antinode at the mid point then there can only be one thing that happens to the amplitude if you move to the right of it (or the left, for that matter.)
You should also know the connection between nodes/antinodes (maxima/minima) and destructive/constructive interference respectively.

Nodes = destructive
Antinodes = constructive

Presumably


So, I'm wondering what would happen with relation to nodes/antinodes, in your view?

What is YOUR view. It seems you want me to answer the question for you.
I've given you as much information as I can.

a) There is constructive interference at the mid point.
You can call it a standing wave antinode. You can also say that at that point the waves meet in phase and the path length from the two speakers is the same. A whole number of wavelengths. Probably what your teacher prefers you to say. It amounts to the same thing.

b) If you move to the left or right of that point you are no longer going to get the antinode. I'm sure you've seen this pattern physically on a string. What do you get if you move to the left or right of an antinode.
Or think of path difference. You have worked out the wavelength of these waves earlier. If there is a maximum at the centre and the path difference is a whole number of wavelengths there, what happens if you move left or right to a place where the path difference is not a whole number, and then move further to a point a wavelength away from the centre where the path difference is again a whole number of waves.

You get a node presumably, which is what I thought..

But regarding the first question in the book, I believe that the trace follows the pattern of the wave normally but I'm not sure what happens after that. What occurs due to the phase lag of one wave in comparison to the other?

Phase lag means phase difference. I've just told you what happens. If the phase difference is a whole wavelength you get constructive interference. If it is half a wavelength you get destructive interference. Antinode and node. Max amplitude and min amplitude.
I told you in an earlier reply that the trace shows the amplitude of the resultant sound wave.

So there's no phase difference at the middle point? Therefore the oscilloscope would just show a straight line?

No. Not a straight line. A phase difference of 1 wavelength (360 degs) is the same as a phase difference of zero. Both mean the waves are in phase. Half a wavelength (180 degs) means the waves are exactly out of phase.
In phase gives constructive interference.
Out of phase gives destructive interference.
Constructive interference gives a maximum amplitude. (Antinode)
Destructive interference gives a minum or zero amplitude. (Node)

In the question, there is zero path difference between the waves at the centre. They have both travelled the same distance in the same medium and have the same wavelength. The waves there are in phase.

So how is it that they become out of phase? And does that occur before we move the microphone?