Wave Energy: Formula, Derivation, Advantages & Disadvantages

Energy is carried by waves. This is demonstrated by the fact that laser waves can be used to eradicate tumours and that ultrasound waves can be utilised to cure medical conditions. As a result, understanding the energy carried by a wave is critical. Let's take a closer look at wave energy and the Energy of a Wave Formula.

Key Terms: Ultrasound, X-ray, Gamma Ray, Joule, Potential Energy, Kinetic Energy

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Mechanical Wave

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A mechanical wave is an oscillating wave of matter that conveys energy across a medium. Although waves can travel enormous distances, the medium of transmission remains immobile. As a result, the oscillating material becomes immobile as well. Mechanical and electromagnetic waves are used to transport energy. Waves and energy both travel in the same direction. To form mechanical waves, a medium must have elasticity and inertia. Modern physics relies heavily on the concepts of mechanical and electromagnetic waves. Wave concepts are used in several theories in quantum electrodynamics and relativity.

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Wave Energy

Wave Energy is a quantity that, when applied to a substance, causes it to heat up or do work. The Joule is the SI unit of energy. James Prescott Joule, a British scientist, gave it his name. The two types of energy are kinetic and potential energy. Water placed in a tank on a building's roof will have energy potential. The water that gushes out when the tap is turned on is the result of the water's potential energy being converted into kinetic energy.

Formula of Wave Energy

\(E = {\rho gH^2 \over 16}\)

Where,

• E is the mean wave energy density
• H is the wave height
• ρ is the water density
• g is the acceleration due to gravity

Formula of Wave Power in terms of wave energy is as follows:

\(P = E_{cg}\)

Where,

• cg is the group velocity in m/s.

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Derivation of Wave Energy

Consider a sinusoidal wave. The energy of a wave is determined by its amplitude and frequency. Kinetic and Potential energy are two types of energy.

Assume a string mass element with mass m. Because the string's linear density is constant, each mass element has the same mass.

Δ m = μΔx

Sum of the kinetic and potential energy of the wave is its total mechanical energy. The kinetic energy is expressed 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 potential energy 

K = 1/4(μA²ω²λ)

Thus, the total energy,

Utotal = Upotential + Ukinetic

=  1/4(μA²ω²λ) + 1/4(μA²ω²λ)

=  1/2(μA²ω²λ)

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Advantages of Mechanical Wave

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• Environmentally friendly energy source: Unlike fossil fuels, wave energy does not release greenhouse gases when it is generated. The turbines use the power of the waves to generate electricity, making them pollution-free and renewable energy sources.
• Wave power, like all alternative energy sources, is a renewable source of energy. Wind causes waves, and the wind is caused by uneven heat on the planet's surface, which is primarily caused by the sun warming at various speeds in different places.
• Waves are a dependable energy source since they are rarely stopped and are almost always in motion. Because the wind does not always blow, wave energy is a more reliable energy source than wind power for generating electricity.
• The amount of kinetic energy exerted by a wave is huge; this energy is absorbed by wave energy converters and used to generate electricity. Because it is always moving and generating energy, the ocean has a lot of potential for energy production.

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Disadvantages of Mechanical Wave

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Wave energy, in addition to its many benefits, has a few drawbacks, which are stated below:

• Because wave energy is still in its early stages of development, largely in research, there is no way to assess the environmental repercussions of large-scale power plants on the shore. Planting plants right on the beach could be damaging since they are ugly and can harm marine life and the ecosystems around them.
• Wave power is an energy technology that is still in its early phases of development, making price speculation impossible. Wave power prices are currently very high because it is still in the research phase of development, but they may come down in the future.
• Costs of maintenance are high: Because these plants will be buried in continually moving saltwater, maintenance is expected to be very costly. Constant movement may result in greater breaking.
• The biggest disadvantage right now is that no utility can install wave farms because they aren't large enough to generate a significant amount of electricity.

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Points to Remember

Following are some important points:

• The strong wind blowing over the ocean's surface causes waves. Electricity is generated by the kinetic energy of waves.
• Wave energy is one of the renewable energies which will be used in the future.
•  Wave energy can be transformed at three different locations in the ocean: offshore, far offshore, and close to shore.
• Because seawater is 850 times denser than air at the same density, wave energy generation plants may produce more energy with a smaller installation.

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