Is it possible to construct and deconstruct magnetic waves? If I have two magnetic waves whose crests and troughs line up, will the two 'cancel' out similar to sound waves?
 A: Any magnetic field has a source and the field lines which represent the magnetic field are closed lines, going in and out of this source:


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*If you approach two sources with the same poles together, you will get an area where both fields are zero. The fields cancel each other out.

*If you approach two sources with the opposite poles together, their field will be united and the field lines are closed lines through both sources.

If I have two magnetic waves whose crests and troughs line up...

If you for sample switch on and of an electromagnet or rotate a permanent magnet you get a swelling magnetic field strength. But even in this case the magnetic field does not leave the source and to talk about this swelling magnetic field as a magnetic wave is misleading. The energy, you loose by your operations, is electromagnetic radiation and not a magnetic wave.

...will the two 'cancel' out similar to sound waves?

No, the magnetic field is attached to it source and can be displaced by another magnetic field, but not dissipated nor canceled out.
A: If you have a compass then they will appear to cancel at that point in time and space but be very careful because the energy of these 2 waves is still present.  They will eventually travel apart and be measurable again.  Just like water waves, 2 opposite moving waves appear to cancel when they collide but if you continue to observe you will see them remerge once they have passed each other.  The terms interference and superposition are used in physics and it gets confused sometimes.
