Wave Fundamentals
5. Wave Energy
Learning Outcomes
- I can explain how waves transfer energy.
- I can relate amplitude to energy carried by a wave.
- I can distinguish between energy transfer and material movement.
- I can compare energy carried by different waves.
- I can describe practical applications of wave energy.
Wave Energy
Waves are important because they can transfer energy from one place to another without transferring matter from one place to another overall. Ocean waves can move floating objects, sound waves can make our eardrums vibrate, and electromagnetic waves from the Sun can transfer enormous amounts of energy across space.
The amount of energy carried by a wave depends on several factors, but one of the most important is its amplitude.
Learning Targets
- I can explain how waves transfer energy.
- I can relate amplitude to energy carried by a wave.
- I can distinguish between energy transfer and material movement.
- I can compare energy carried by different waves.
- I can describe practical applications of wave energy.
Waves Transfer Energy
A wave is a travelling disturbance that transfers energy.
Consider dropping a stone into a pond.
Ripples spread outward from where the stone enters the water.
The disturbance travels across the surface and carries energy away from the point where the stone entered.
If the ripple reaches a floating leaf, the leaf may begin to move.
The moving leaf provides evidence that energy has reached it.
The energy has travelled across the water as a wave.
However, this does not mean that the water itself travelled all the way from the stone to the leaf.
Energy Transfer Is Not the Same as Matter Transfer
This is one of the most important ideas in wave physics:
Waves transfer energy without an overall transfer of matter.
Consider a wave travelling along a rope.
If you move one end of the rope up and down, a wave travels along it.
Individual sections of the rope move:
Up and down
but the wave travels:
Along the rope
The rope itself does not travel from one end to the other.
Instead, neighbouring sections interact and pass the disturbance — and therefore energy — along the rope.
A Stadium Wave
A stadium wave provides a useful model.
People in the stadium stand up and sit down.
Each person moves only a small distance.
However, the pattern travels around the stadium.
The people do not travel around the stadium with the wave.
Similarly, particles in a medium usually oscillate around their equilibrium positions while the wave disturbance travels through the medium.
Mechanical Waves and Energy
Mechanical waves require a medium through which to travel.
Examples include:
- Sound waves
- Water waves
- Waves on ropes
- Seismic waves
- Waves through springs
The particles of the medium interact with neighbouring particles, allowing energy to move through the material.
Without a medium, mechanical waves cannot propagate.
For example, sound cannot travel through a vacuum.
Sound Transfers Energy
When a speaker produces sound, its surface vibrates.
The vibrating speaker causes nearby air particles to oscillate.
These particles interact with neighbouring particles, producing alternating regions of:
- Compression
- Rarefaction
The disturbance travels through the air as a sound wave.
When the sound reaches your ear, it transfers energy to your eardrum and causes it to vibrate.
The air molecules themselves do not travel all the way from the speaker to your ear.
Electromagnetic Waves Transfer Energy
Electromagnetic waves can transfer energy without requiring a material medium.
Examples include:
- Radio waves
- Microwaves
- Infrared
- Visible light
- Ultraviolet
- X-rays
- Gamma rays
This means electromagnetic waves can transfer energy through a vacuum.
Energy from the Sun travels approximately 150 million kilometres through space before reaching Earth.
Much of this energy is carried by electromagnetic radiation.
Amplitude and Energy
Amplitude is the maximum displacement of a point from its equilibrium position.
A wave with a greater amplitude generally carries more energy than a similar wave with a smaller amplitude.
For example, compare two waves travelling along identical ropes.
Wave A has a small amplitude.
Wave B has a much larger amplitude.
The source producing Wave B must move the rope through a greater displacement and do more work on it.
Wave B therefore transfers more energy.
Energy and Amplitude Squared
For many types of waves under the same conditions, the energy transferred is related to the square of the amplitude.
We can represent this approximately as:
Energy ∝ amplitude²
This means the relationship is not simply:
Double amplitude → double energy
Instead:
Double amplitude → about four times the energy
because:
2² = 4
Similarly:
Triple amplitude → about nine times the energy
because:
3² = 9
This relationship applies when comparing otherwise similar waves under conditions where the usual amplitude-squared relationship holds.
Worked Example — Doubling Amplitude
Wave A has amplitude:
2 cm
Wave B has amplitude:
4 cm
Wave B has twice the amplitude of Wave A.
If energy is proportional to amplitude squared:
Energy ratio = 2²
Energy ratio = 4
Therefore:
Wave B carries approximately four times as much energy as Wave A, assuming the other relevant properties are unchanged.
Worked Example — Tripling Amplitude
Suppose one wave has three times the amplitude of another similar wave.
Using:
Energy ∝ amplitude²
we get:
Energy ratio = 3²
Energy ratio = 9
The larger-amplitude wave therefore carries approximately:
9 times as much energy
under the same conditions.
This is why relatively small changes in amplitude can produce large changes in energy transfer.
Amplitude Is Not Wavelength
Amplitude and wavelength describe different properties.
Amplitude measures maximum displacement from equilibrium.
Wavelength measures the distance between corresponding points on consecutive waves.
A wave can have:
- Large amplitude and long wavelength
- Large amplitude and short wavelength
- Small amplitude and long wavelength
- Small amplitude and short wavelength
Changing amplitude does not automatically mean wavelength changes.
Energy in Water Waves
Water waves transfer energy across the surface of water.
This can be seen clearly when waves reach a coastline.
Large waves can:
- Move objects
- Erode coastlines
- Damage structures
- Move sediment
- Rock boats
The water particles themselves undergo complicated oscillatory motion rather than simply travelling across the ocean with the wave.
The wave energy can nevertheless travel great distances.
Energy in Sound Waves
Sound waves also carry energy.
A quiet sound produces relatively small variations in pressure and particle displacement.
A louder sound generally has a larger amplitude.
Therefore:
Greater sound-wave amplitude → greater intensity
This explains why powerful sound waves can physically affect objects.
At sufficiently high intensities, sound can even damage structures or biological tissue.
Energy in Seismic Waves
Earthquakes release large amounts of energy.
Some of this energy travels through Earth as seismic waves.
Seismic waves can:
- Shake buildings
- Move the ground
- Damage structures
- Trigger landslides
Scientists also use seismic waves to investigate Earth's internal structure.
Their behaviour provides information about materials deep inside the planet.
Comparing the Energy of Waves
When comparing similar waves, amplitude provides an important indication of the amount of energy being transferred.
Suppose two waves travel through the same medium and have the same frequency.
Wave A has amplitude:
1 cm
Wave B has amplitude:
3 cm
The amplitude ratio is:
3 : 1
If energy is proportional to amplitude squared:
Energy ratio = 3² : 1²
Energy ratio = 9 : 1
Wave B therefore carries approximately nine times as much energy as Wave A under these conditions.
Frequency Can Also Matter
Amplitude is not the only property that can affect the energy carried by a wave.
The relationship between energy and frequency depends on the type of wave and the situation.
For electromagnetic radiation, the energy associated with an individual photon is:
E = hf
where:
- E = photon energy
- h = Planck's constant
- f = frequency
Therefore, higher-frequency electromagnetic radiation has greater energy per photon.
This is one reason ultraviolet, X-rays, and gamma rays can have very different effects from radio waves or microwaves.
Energy Can Spread Out
As a wave travels away from its source, its energy may spread over a larger area.
This often causes the wave's intensity to decrease with distance.
Consider sound from a speaker.
Close to the speaker, the sound is relatively intense.
Farther away, the sound becomes weaker.
The source has not necessarily started producing less energy.
Instead, the wave's energy is distributed over an increasingly large region.
Absorption
Waves can also lose energy from the wave itself through absorption.
When a material absorbs wave energy, that energy is transferred into other energy stores, often increasing the material's internal energy.
For example:
Sunlight strikes a dark surface.
The surface absorbs some of the electromagnetic radiation.
Its temperature increases.
The energy has not disappeared.
It has been transferred from the electromagnetic wave into the material.
Reflection, Transmission, and Absorption
When a wave reaches a boundary, several things may happen.
Some energy may be:
Reflected
Some may be:
Transmitted
Some may be:
Absorbed
The total energy is conserved.
Energy may change form or move into different parts of the system, but it is not created or destroyed.
Practical Application — Solar Energy
Solar panels use energy transferred by electromagnetic waves from the Sun.
Sunlight reaches a photovoltaic cell.
The cell converts some of the incoming electromagnetic energy into electrical energy.
The energy pathway can be summarized as:
Sun → electromagnetic waves → solar panel → electrical energy
Not all incoming energy becomes useful electrical energy.
Some is reflected or transferred to thermal energy stores.
Practical Application — Ultrasound
Ultrasound uses high-frequency sound waves.
In medical imaging, ultrasound waves are sent into the body.
Some of the waves are reflected when they encounter boundaries between different tissues.
The returning waves are detected and processed to create an image.
Ultrasound therefore uses the transfer and reflection of wave energy to obtain information about structures inside the body.
Practical Application — Sonar
Sonar uses sound waves travelling through water.
A sound pulse is transmitted.
The pulse travels through the water and reflects from an object.
The returning echo is detected.
Sonar can be used to:
- Measure water depth
- Locate underwater objects
- Map the ocean floor
- Detect schools of fish
The system relies on sound waves transferring energy through water and returning some of that energy to the detector.
Practical Application — Communication
Electromagnetic waves are essential to modern communication.
Different parts of the electromagnetic spectrum are used for:
- Radio
- Television
- Mobile phones
- Wi-Fi
- Satellite communication
- Fibre-optic communication
The waves transfer energy, but they can also be modified to carry information.
Practical Application — Microwave Heating
Microwaves are electromagnetic waves.
In a microwave oven, electromagnetic energy is transferred to food, especially through interactions with polar molecules such as water.
This increases the food's internal energy and temperature.
The energy transfer can be represented as:
Electrical energy → electromagnetic waves → internal energy of food
This is another example of waves being used deliberately to transfer energy.
Practical Application — Wave Power
Ocean waves contain mechanical energy that can potentially be converted into useful electrical energy.
Wave-energy devices can use the movement of water to operate:
- Turbines
- Generators
- Hydraulic systems
The energy transfer might be represented as:
Ocean-wave energy → mechanical motion → generator → electrical energy
Wave power is therefore a direct example of humans capturing energy transported by waves.
Practical Application — Earthquake Engineering
Engineers need to understand how seismic waves transfer energy through the ground and into buildings.
When seismic waves reach a structure, they can cause the ground and building to oscillate.
Earthquake-resistant buildings may use:
- Flexible structures
- Dampers
- Base isolation
- Reinforced frameworks
These systems help control how seismic energy is transferred through the structure.
Energy Transfer and Conservation of Energy
Waves do not create energy.
The energy carried by a wave must come from somewhere.
For example, when you shake a rope:
Chemical energy in your body
is transferred mechanically to:
The rope
and then travels along the rope as:
Wave energy
Eventually much of this energy may be transferred to the surroundings as thermal energy.
The total amount of energy is conserved.
Worked Example — Comparing Wave Energy
Two otherwise similar waves have amplitudes:
Wave A = 2 mm
Wave B = 6 mm
Find the amplitude ratio:
6 / 2 = 3
Wave B has three times the amplitude.
If:
Energy ∝ amplitude²
then:
Energy ratio = 3²
Energy ratio = 9
Therefore:
Wave B transfers approximately nine times as much energy as Wave A.
Worked Example — Finding an Amplitude Change
Suppose a wave transfers four times as much energy as another otherwise similar wave.
If:
Energy ∝ amplitude²
then:
4 = amplitude ratio²
The amplitude ratio is:
2
Therefore, the higher-energy wave has:
Twice the amplitude
of the original wave.
Wave Energy in Everyday Life
Wave energy transfers occur around us constantly.
When you:
- Hear music, sound waves transfer energy to your ears.
- Feel sunlight, electromagnetic waves transfer energy to your skin.
- Use Wi-Fi, electromagnetic waves travel between devices.
- Speak, your vocal cords create sound waves.
- Watch television, light waves transfer energy to your eyes.
- Use a microwave oven, microwaves transfer energy into food.
- See ripples in water, mechanical waves carry energy across the surface.
Wave physics is therefore not limited to laboratories. It is fundamental to everyday life and modern technology.
Common Mistakes
Mistake: Thinking particles travel with the wave
Particles usually oscillate around equilibrium positions while energy travels through the system.
Mistake: Thinking waves transfer matter
Waves can cause local movement of matter, but there is generally no overall transport of the medium with the wave.
Mistake: Thinking amplitude and energy are the same thing
Amplitude is a measure of displacement.
Energy is the capacity to cause change or do work.
Amplitude provides information about the energy carried by otherwise comparable waves.
Mistake: Assuming twice the amplitude means twice the energy
For many waves under comparable conditions:
Energy ∝ amplitude²
Therefore, doubling amplitude can correspond to approximately four times the energy.
Mistake: Thinking energy disappears when a wave gets weaker
Energy may have:
- Spread over a larger area
- Been absorbed
- Been reflected
- Been transferred into another energy store
Energy is conserved.
Mistake: Thinking electromagnetic waves require matter
Electromagnetic waves can travel through a vacuum.
Mechanical waves require a medium.
Key Terms
Wave energy – energy transferred by a wave.
Amplitude – maximum displacement from equilibrium.
Medium – material through which a mechanical wave travels.
Oscillation – repeated motion around an equilibrium position.
Mechanical wave – a wave that requires a medium.
Electromagnetic wave – a wave that can travel through a vacuum.
Intensity – power transferred per unit area.
Absorption – transfer of wave energy into a material.
Reflection – when a wave returns from a boundary.
Transmission – when a wave passes through a boundary or material.
Seismic wave – a wave carrying energy through Earth.
Ultrasound – sound with a frequency above the upper limit of normal human hearing.
Check Your Understanding
1. What does a wave transfer from one location to another?
2. Explain why a wave can transfer energy without transferring matter overall.
3. Describe what happens to individual sections of a rope when a transverse wave travels along it.
4. How is the amplitude of a wave related to the amount of energy it carries?
5. Two otherwise identical waves have amplitudes of 2 cm and 4 cm. Approximately how many times more energy does the larger-amplitude wave carry?
6. One wave has three times the amplitude of another similar wave. Approximately how many times as much energy does it carry?
7. Explain the difference between amplitude and wavelength.
8. Describe how sound transfers energy from a speaker to your ear.
9. Why can electromagnetic waves transfer energy from the Sun to Earth even though most of the space between them is a vacuum?
10. What can happen to wave energy when a wave reaches a boundary?
11. Explain how ultrasound uses wave energy in medical imaging.
12. Describe one way humans can convert energy carried by waves into useful electrical energy.
Key Takeaways
- Waves transfer energy from one place to another.
- Waves generally do this without an overall transfer of the material through which they travel.
- Particles in a medium usually oscillate around equilibrium positions while the disturbance travels.
- Mechanical waves require a medium.
- Electromagnetic waves can transfer energy through a vacuum.
- Greater amplitude generally means greater energy transfer for otherwise similar waves.
- For many waves, energy is approximately proportional to amplitude squared.
- Doubling amplitude can therefore correspond to approximately four times the energy.
- Wave energy may be reflected, transmitted, absorbed, or spread over a larger area.
- Energy transferred by waves obeys the principle of conservation of energy.
- Sound, ultrasound, seismic waves, sunlight, communications, sonar, and ocean-wave power all demonstrate practical uses or effects of wave energy.
- Understanding wave energy is important in medicine, communications, renewable energy, engineering, astronomy, and everyday life.
Did You Know?
A large ocean swell can travel thousands of kilometres across an ocean while individual water particles remain relatively close to their original locations. What travels across the ocean is primarily the wave disturbance and its energy, not the same body of water moving all the way from one coastline to another.