Do waves transfer energy or matter?
A wave is a disturbance that transfers energy from one place to another without transferring matter.
To summarise, waves carry energy. The amount of energy they carry is related to their frequency and their amplitude. The higher the frequency, the more energy, and the higher the amplitude, the more energy.
A wave transports its energy without transporting matter. Waves are seen to move through an ocean or lake; yet the water always returns to its rest position. Energy is transported through the medium, yet the water molecules are not transported.
Mechanical Waves
Waves transfer energy from one place to another, but they do not necessarily transfer any mass. Light, sound, and waves in the ocean are common examples of waves. Sound and water waves are mechanical waves; meaning, they require a medium to travel through.
Waves transfer energy, momentum, and information, but not mass. A naive description of a wave is that it has something to do with motion. But the motion of a wave on the water is not the same as the motion of the water from a hose. When waves move over the surface of the ocean, where does the ocean go?
Waves transfer energy but not matter. The particles take part in the propagation of wave by transferring the disturbance from one particle to another. Hence, the energy is transferred, but the position of the particles remains unchanged over time.
All waves carry energy. The energy of some waves, such as the energy of earthquakes, can be directly observed.
The total mechanical energy of the wave is the sum of its kinetic energy and potential energy. The kinetic energy comes out as, K = 1/4(μA2ω2λ), where A is the amplitude of the wave (in metres), ω is the angular frequency of the wave oscillator(in hertz), λ is the wavelength (in metres).
The wave function for a material particle is often called a matter wave. The relationship between momentum and wavelength for matter waves is given by p = h/λ, and the relationship energy and frequency is E = hf.
Light exists in tiny packets called photons. Photons have no rest mass and they do not occupy any volume. So light is not matter. It is the radiation of energy.
Can waves carry mass?
Sound waves do carry mass. Using a theoretical approach called effective field theory, which is commonly used in particle and solid-state physics, the team calculated the mass carried by a sound wave packet propagating though a superfluid.
Water and sound waves are mechanical and require a medium in order to travel. Light and radio waves are not mechanical but rather electromagnetic and do not need a medium.

In fact, if we can define it, we can quantify just how “wave-like” a particle or set of particles is. Even an entire human being, under the right conditions, can act like a quantum wave.
Light Is Also a Particle!
Now that the dual nature of light as "both a particle and a wave" has been proved, its essential theory was further evolved from electromagnetics into quantum mechanics. Einstein believed light is a particle (photon) and the flow of photons is a wave.
The significance of the de Broglie relationship is that it proved mathematically that matter can behave as a wave. In layman's terms, the de Broglie equation says that every moving particle – microscopic or macroscopic –has its own wavelength. For microscopic objects, the wave nature of matter is observable.
Light can be described both as a wave and as a particle. There are two experiments in particular that have revealed the dual nature of light. When we're thinking of light as being made of of particles, these particles are called “photons”. Photons have no mass, and each one carries a specific amount of energy.
In life, the human body comprises matter and energy. That energy is both electrical (impulses and signals) and chemical (reactions). The same can be said about plants, which are powered by photosynthesis, a process that allows them to generate energy from sunlight.
Radio waves, light, and other forms of radiation all have energy, but do not need matter. So yes, you absolutely can have energy without matter, in empty space.
Water is matter, just like anything else. So the water cycle transports matter. Whether water is in the form of a liquid, a gas (water vapor), or a solid (snow), it's still matter. But it turns out that the water cycle also transports energy.
Energy Transportation
Since the particles of the medium itself don't move, just vibrate, waves are said to be a type of energy transport phenomenon. This means that a disturbance moves through a medium particle to particle, moving energy across a distance during this process.
Do waves carry energy and water?
In reality, the water in waves doesn't travel much at all. The only thing waves do transmit across the sea is energy.
Waves have a lot of energy
Ocean waves contain tremendous energy. The theoretical annual energy potential of waves off the coasts of the United States is estimated to be as much as 2.64 trillion kilowatthours, or the equivalent of about 64% of total U.S. utility-scale electricity generation in 2021.
Wave power is typically produced by floating turbine platforms or buoys that rise and fall with the swells. However, wave power can be generated by exploiting the changes in air pressure occurring in wave capture chambers that face the sea or changes in wave pressure on the ocean floor.
When waves travel through matter, they lose some energy to the matter as they pass through it. But when waves travel through space, no energy is lost.
Waves are usually formed when water is pushed by winds. In other words, wind energy creates waves. Waves can also be formed by energy from earth movements, such as an underwater earthquake. The water itself does not really flow along with the wave, but instead moves in a rolling fashion as the energy passes through it.