When two transverse waves traveling through a medium meet and exactly coincide, the resulting displacement of the medium is determined by the principle of superposition.

Superposition Principle: When two or more waves meet at a point, the resultant displacement of the medium at that point is the vector sum of the displacements of the individual waves.

In the case of two waves coinciding exactly:

* If the waves are in phase: This means their crests and troughs align perfectly. The resulting displacement will be the sum of the individual displacements. The amplitude of the resulting wave will be twice the amplitude of either individual wave.

* If the waves are out of phase: This means the crests of one wave align with the troughs of the other. The resulting displacement will be the difference of the individual displacements. If the waves have equal amplitudes, the resulting displacement will be zero, and the medium will appear undisturbed at that point.

Therefore, the resulting displacement of the medium depends on the phase relationship between the two waves.

Here are some key points to remember:

* Constructive Interference: When waves in phase meet, the amplitude increases.

* Destructive Interference: When waves out of phase meet, the amplitude decreases.

* Complete Destructive Interference: If waves of equal amplitude and opposite phase meet, they completely cancel each other out.