In classical physics, waves are typically described as a propagation of energy through a medium or a field. While particles are not a strict requirement for the existence of waves in classical physics, they often play a role in mediating or carrying the energy of the wave.
However, in the realm of quantum mechanics, which deals with the behavior of particles at the smallest scales, the concept of wave-particle duality arises. According to quantum mechanics, particles can exhibit wave-like properties and vice versa. This means that in certain situations, such as in quantum field theory, waves can be described by the behavior of underlying particles.
In empty space devoid of matter, there can still exist fields that can support wave-like behavior. For example, the electromagnetic field can propagate as electromagnetic waves, even in the absence of particles. These waves are known as electromagnetic radiation and can include various forms like light, radio waves, microwaves, and X-rays.
So, while waves can exist without particles in the classical sense, the quantum nature of particles and fields means that the relationship between waves and particles is more complex and intertwined at the fundamental level.