Wave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds significant promise for renewable energy generation.
Physics defines the capability of doing work as a concept called energy. Energy also follows the law of conservation that is "energy cannot be created and can not be destroyed". Heat, light, and sound all are forms of energy. Energy also follows some rule to move from one body to another.
Whenever energy has been transferred, it is always designated according to its nature. This states that energy always changes its form if required like electric energy got converted into light when a bulb is lightened, similarly wind energy can be converted to mechanical and then electrical in windmills.
A wave is a disturbance/ movement of particles in a medium that transports energy without causing net particle movement. Elastic deformation, pressure variations, electric or magnetic field, electronic potential, or temperature variations are all examples.
Large-amplitude earthquakes result in significant ground displacements.
Loud sounds have high-pressure amplitudes, originating from larger-amplitude source vibrations than softer sounds.
High-frequency waves deliver more energy packets per unit of time compared to low-frequency waves.
If two mechanical waves have equal amplitudes but one has twice the frequency of the other, the higher-frequency wave transfers energy at a rate four times greater.
The main components of wave energy are Kinetic energy and Potential energy.
A string is attached to the rod of the string vibrator, which produces a sinusoidal wave in the string, with a wave velocity v. A section of the string with mass Δm oscillates at the same frequency as the wave.
Kinetic Energy Component
The Formula of Kinetic energy is,
Ukinetic = mv2 / 2
Let v be the velocity of the wave.
Since, velocity has two component vx (horizontal component in direction of motion of wave) and vy (perpendicular component perpendicular to motion of wave).
So, the kinetic energy of each mass element of the string is,
ΔUkinetic = 1/2 (Δm) vy2
as the mass element oscillates perpendicular to the direction of the motion of the wave.
If the density of string is μ, then the mass of element (Δx) of string,
Δm = μΔx
Hence, Kinetic energy is:
ΔUkinetic = 1/2 (μΔx)vy2
For total kinetic energy of wave we have,
Ukinetic = 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).
Potential Energy Component
In Oscillations, the potential energy stored in a spring with a linear restoring force is,
U = 1/2ksx2
where the equilibrium position is defined at x = 0 m.
The potential energy of the mass element is,
U = 1/2ksx2
= 1/2 Δmw2x2
= 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).
Hence, the Total Wave Energy
Utotal = Upotential + Ukinetic
= 1/4(μA2ω2λ) + 1/4(μA2ω2λ)
Utotal = 1/2(μA2ω2λ)
where A is the amplitude of the wave (in metres), ω the angular frequency of the wave oscillator(in hertz), and λ the wavelength (in metres).
Problem 1: For a wave with given values, amplitude A = 10 m, angular frequency, ω = 50 Hz, wavelength λ = 10 m, and string density μ = 200. Find the wave energy by using Wave Energy Formula.
Solution:
Utotal = 1/2 (200 × 10 × 10 × 50 × 50 × 10)
= 2500000 J
= 2.5 MJ
Problem 2: Describe the components of wave energy.
Solution:
Wave energy has two components kinetic energy of wave particles and potential energy.
