Waves appear in nature and are described by wave equations,
second-order linear partial differential equation for the description of waves – as they occur in physics
All such equations have time dependent solutions and what they have in common is the oscillating behaviour in time that allows to assign a wavelength and describe the waves observed.
Now in quantum mechanics the description of the behavior of nature is dependent on differential equations of this type. The first studied is the Schrodinger equation and the link provides a good historical description of how it became evident that in the microcosm the behavior of particles was following a wave equation.
What is important to keep in mind is that in quantum mechanics the waves are probability waves, i.e. the probability if you do an experiment, like the double slit experiment, to find a particle in space at the time you look is governed by a wave solution. This is in contrast to other waves in physics which are variations in time on a medium, or in classical electromagnetism on changing fields.
So the relationship is the mathematical formulation of the differential equations describing nature in the two frameworks, not a one to one correspondence.
As I mentioned in my comment in electromagnetism, the frequency of the electromagnetic field described by classical electrodynamics appears in the energy of the photon ( the particle form of electromagnetism) in the identity E=h.nu. The interference pattern seen in the double slit experiment will display the frequency of light nu. If you continue your studies in physics you will be able to understand how the microcosm described by quantum mechanics leads to the macrocosm we call "classical physics" smoothly.