Amplitude is one of the fundamental properties of waves in physics. It helps explain how far a vibrating particle moves from its equilibrium position and plays an important role in understanding wave energy, intensity, sound and light.

In IB Physics, amplitude is more than just the height of a wave. Students need to recognise it on different graphs, distinguish it from wavelength, understand how it relates to energy and apply the concept when answering examination questions.

This guide explains amplitude step by step, with definitions, formulas, worked examples, graph interpretation, common mistakes and practical applications to help students build a clear understanding of wave behaviour.

Quick Amplitude Checklist for IB Physics

Before solving a wave-related problem, remember these important points:

• Amplitude is the maximum displacement from the equilibrium position.
• It is measured from the equilibrium line to a crest or trough in a transverse wave.
• The vertical distance from a crest to a trough is twice the amplitude, or (2A).
• Amplitude is different from wavelength, which measures the distance between corresponding points on consecutive waves.
• In many wave systems, energy transported and intensity are proportional to the square of the amplitude.
• Increasing amplitude does not automatically increase wave speed in the basic wave models studied at this level.
• In longitudinal waves, such as sound in air, amplitude can be described through the maximum pressure or density variation from equilibrium.
• On a displacement-time or displacement-position graph, amplitude is the maximum vertical displacement from the equilibrium line.

What Does Amplitude Mean in IB Physics?

In IB Physics, amplitude (A) is the maximum displacement of a point in a medium from its equilibrium position during an oscillation.

The equilibrium position is the point where the particle would rest if it were not oscillating. As a wave travels, particles in the medium move or oscillate around this position.

The maximum distance a particle moves away from its equilibrium position is called the amplitude.

For a transverse wave, the amplitude is measured from the equilibrium line to the highest point (crest) or lowest point (trough).

Two words are particularly important when defining amplitude:

• Maximum: Amplitude represents the greatest displacement, not the average or usual displacement.
• Equilibrium: The measurement must begin from the central or resting position, not from another point on the wave.

For example, if a wave has a maximum displacement of 4 cm from its equilibrium position, its amplitude is 4 cm.

If the vertical distance between the crest and trough is 8 cm, the amplitude is 4 cm, not 8 cm.

Amplitude Formula

The basic relationship between amplitude and maximum displacement is:

[
A = \text{Maximum displacement from equilibrium}
]

Where:

• (A) = amplitude
• Maximum displacement = greatest distance from the equilibrium position

Amplitude is measured in units of displacement, such as metres (m), centimetres (cm) or millimetres (mm).

Amplitude in Transverse and Longitudinal Waves

Amplitude can be understood differently depending on the type of wave. The main distinction is between transverse waves and longitudinal waves.

1. Amplitude in Transverse Waves

In a transverse wave, particles oscillate perpendicular to the direction in which the wave travels.

Examples include:

• Waves travelling along a stretched string.
• Water surface waves in the simplified wave model.
• Electromagnetic waves, including light.

For a transverse wave, amplitude is the maximum displacement of a particle from its equilibrium position. On a typical displacement graph, this is the vertical distance from the equilibrium line to a crest or trough.

A wave with a larger amplitude has a greater maximum displacement than a wave with a smaller amplitude.

2. Amplitude in Longitudinal Waves

In a longitudinal wave, particles oscillate parallel to the direction in which the wave travels.

Sound waves travelling through air are a common example.

As a sound wave moves through air, it creates regions of:

• Compression: Areas where air particles are closer together and pressure or density is higher than the equilibrium value.
• Rarefaction: Areas where air particles are farther apart and pressure or density is lower than the equilibrium value.

For a longitudinal sound wave, amplitude can be described using the maximum pressure variation or density variation from the equilibrium value.

This is important because a longitudinal wave does not have the same visible crest-and-trough shape as a transverse wave.

Why Does Amplitude Matter? Understanding Energy and Intensity

Amplitude is important because it is closely connected to the energy transported by a wave.

For many wave systems under appropriate conditions, the energy transported and the intensity of the wave are proportional to the square of its amplitude.

The relationship is:

[
E \propto A^2
]

Similarly, for a wave under comparable conditions:

[
I \propto A^2
]

Where:

• (E) = energy transported by the wave
• (I) = intensity
• (A) = amplitude

This means that a change in amplitude can produce a much larger change in energy or intensity.

How Does Doubling Amplitude Affect Energy?

Consider a wave whose original amplitude is (A).

If its amplitude doubles, the new amplitude becomes (2A).

Using the square relationship:

[
\frac{E_2}{E_1} = \frac{(2A)^2}{A^2}
]

[
\frac{E_2}{E_1} = 4
]

Therefore, doubling the amplitude makes the energy four times greater, assuming the other relevant conditions remain unchanged.

Similarly:

• If amplitude triples, energy becomes nine times greater.
• If amplitude is halved, energy becomes one-quarter of its original value.

How Is Amplitude Related to Loudness and Brightness?

Amplitude helps explain several familiar wave-related observations.

Sound and loudness

For sound waves, a greater pressure amplitude generally corresponds to greater sound intensity and perceived loudness, assuming other conditions remain comparable.

A louder sound is therefore generally associated with a sound wave having a larger pressure amplitude.

Light and brightness

For electromagnetic waves, intensity is related to the square of the electric field amplitude.

A larger electric field amplitude corresponds to greater intensity under comparable conditions. This can be associated with greater brightness when the light is visible and other viewing conditions remain the same.

Important: The relationship between amplitude and intensity should not be confused with the relationship between amplitude and wave speed. They describe different wave properties.

How to Find Amplitude on a Wave Graph

Wave graphs are commonly used in IB Physics to test whether students understand amplitude, wavelength, frequency and displacement.

The most important step is to identify the equilibrium line before measuring the amplitude.

There are two common types of displacement graphs.

1. Displacement-Time Graph

A displacement-time graph shows how the displacement of one point in a medium changes as time passes.

The horizontal axis represents time, while the vertical axis represents displacement.

To find amplitude:

1. Identify the equilibrium position, usually represented by the zero-displacement line.
2. Find the highest point or crest on the graph.
3. Measure the vertical distance from the equilibrium line to the crest.
4. This maximum vertical displacement is the amplitude.

You can also measure from the equilibrium line to the lowest point or trough. The result should be the same for an ideal sinusoidal wave.

For example, if the maximum displacement shown on a displacement-time graph is 0.06 m, the amplitude is:

[
A = 0.06\text{ m}
]

2. Displacement-Position Graph

A displacement-position graph shows how the displacement of different points in a medium varies with position at one particular instant.

The horizontal axis represents position, while the vertical axis represents displacement.

To calculate amplitude:

1. Identify the equilibrium line.
2. Locate the highest crest or lowest trough.
3. Measure the maximum vertical distance from the equilibrium line.
4. Record this distance as the amplitude.

Remember that the horizontal distance between two consecutive crests represents the wavelength, not the amplitude.

Amplitude vs Wavelength

Amplitude and wavelength are two different properties of a wave.

• Amplitude: Maximum vertical displacement from the equilibrium position.
• Wavelength ((\lambda)): Distance between two consecutive points that are in the same phase, such as two neighbouring crests.

Amplitude is measured vertically on a standard displacement graph, while wavelength is measured horizontally.

Understanding this difference is particularly important when interpreting displacement-time and displacement-position graphs.

Common Amplitude Mistakes in IB Physics

Amplitude questions may look straightforward, but students often lose marks because they confuse basic wave properties or overlook important details.

Here are some common mistakes and how to avoid them.

1. Measuring from Crest to Trough

Mistake: Treating the entire vertical distance from a crest to a trough as the amplitude.

Correct approach: Amplitude is measured from the equilibrium position to a crest or trough.

The crest-to-trough distance is (2A), not (A).

2. Confusing Amplitude with Wavelength

Mistake: Assuming amplitude and wavelength measure the same thing.

Correct approach: Amplitude measures maximum displacement, whereas wavelength measures the distance between corresponding points on consecutive waves.

3. Assuming Amplitude Determines Wave Speed

Mistake: Thinking that increasing amplitude automatically makes a wave travel faster.

Correct approach: In the basic wave models studied in IB Physics, wave speed depends on the properties of the medium and the type of wave. For example, the speed of a wave on a stretched string depends on its tension and linear mass density.

Amplitude does not automatically determine wave speed.

4. Ignoring Damping

Mistake: Assuming that a wave or oscillation always maintains the same amplitude.

Correct approach: In real systems, damping can cause amplitude to decrease over time because energy is transferred to the surroundings, often through effects such as friction or resistance.

For example, a swinging pendulum gradually loses amplitude as it moves through air resistance and friction at its support.

5. Forgetting the Equilibrium Position

Mistake: Measuring amplitude from an arbitrary point on the graph.

Correct approach: Always identify the equilibrium line first. The maximum displacement must be measured from this reference position.

How Amplitude Connects to Standing Waves and Interference

Amplitude also plays an important role when two or more waves overlap.

Two important wave phenomena are interference and standing waves.

1. Amplitude and Interference

Interference occurs when two or more waves overlap and combine.

The resulting displacement depends on the principle of superposition.

There are two main types of interference:

Constructive interference

Constructive interference occurs when waves combine in such a way that their displacements reinforce each other.

When two waves of equal amplitude meet in phase, their resultant amplitude can be twice the amplitude of either individual wave.

Destructive interference

Destructive interference occurs when waves combine in such a way that their displacements oppose each other.

When two waves of equal amplitude meet completely out of phase, their resultant displacement can be zero.

This is why amplitude is important when studying how waves interact.

2. Amplitude in Standing Waves

A standing wave forms when two waves of the same frequency and similar amplitude travel in opposite directions and interfere.

Unlike a travelling wave, the amplitude of a standing wave varies with position.

Two important points in a standing wave are:

• Nodes: Points where the displacement is always zero. Nodes have zero amplitude.
• Antinodes: Points where the maximum displacement is greatest. Antinodes have maximum amplitude.

The distance between two consecutive nodes is half a wavelength.

Understanding amplitude at nodes and antinodes helps students interpret standing-wave diagrams and solve related wave problems.

Solved Examples on Amplitude in Physics

The best way to understand amplitude is to apply the concept to numerical and graph-based questions.

Example 1: Finding Amplitude from Maximum Displacement

A particle in a wave moves a maximum distance of 5 cm from its equilibrium position. Calculate the amplitude.

Solution:

Amplitude is the maximum displacement from equilibrium.

[
A = 5\text{ cm}
]

Answer: The amplitude is 5 cm.

Example 2: Finding Amplitude from Crest-to-Trough Distance

A transverse wave has a vertical distance of 12 cm between its crest and trough. Calculate its amplitude.

Solution:

The distance from crest to trough is twice the amplitude.

[
2A = 12
]

[
A = \frac{12}{2}
]

[
A = 6\text{ cm}
]

Answer: The amplitude is 6 cm.

Example 3: Comparing Energy When Amplitude Changes

A wave has an amplitude of 2 cm. Its amplitude is increased to 6 cm. Calculate the factor by which its energy increases, assuming the energy is proportional to the square of the amplitude.

Solution:

The energy relationship is:

[
E \propto A^2
]

The ratio of the new energy to the original energy is:

[
\frac{E_2}{E_1} = \frac{A_2^2}{A_1^2}
]

Substitute the values:

[
\frac{E_2}{E_1} = \frac{6^2}{2^2}
]

[
= \frac{36}{4}
]

[
= 9
]

Answer: The energy becomes nine times greater.

Example 4: Identifying Amplitude from a Displacement-Time Graph

A displacement-time graph shows that a particle reaches a maximum displacement of 0.08 m above its equilibrium position and a minimum displacement of 0.08 m below it. Find the amplitude.

Solution:

Amplitude is the maximum displacement from equilibrium.

[
A = 0.08\text{ m}
]

Answer: The amplitude is 0.08 m.

Example 5: Comparing Two Waves

Wave P has an amplitude of 3 cm, while Wave Q has an amplitude of 6 cm. Assuming both waves have the same relevant conditions, compare their intensities if intensity is proportional to amplitude squared.

Solution:

[
\frac{I_Q}{I_P} = \frac{A_Q^2}{A_P^2}
]

[
= \frac{6^2}{3^2}
]

[
= \frac{36}{9}
]

[
= 4
]

Answer: Wave Q has four times the intensity of Wave P.

Practice Questions on Amplitude

Test your understanding with these IB Physics-style questions.

Question 1: A wave has a maximum displacement of 0.12 m from its equilibrium position. What is its amplitude?

Question 2: The distance between the crest and trough of a transverse wave is 18 cm. Calculate its amplitude.

Question 3: A wave's amplitude increases from 4 cm to 8 cm. By what factor does its energy increase, assuming energy is proportional to amplitude squared?

Question 4: Explain the difference between amplitude and wavelength.

Question 5: What happens to the amplitude of a damped oscillation over time?

Answers:

1. 0.12 m.
2. 9 cm.
3. Four times greater.
4. Amplitude is maximum displacement from equilibrium; wavelength is the distance between consecutive points in the same phase.
5. The amplitude gradually decreases as energy is transferred to the surroundings.

Frequently Asked Questions About Amplitude in Physics

1. Does amplitude affect wave speed in IB Physics?

In the basic wave models studied in IB Physics, amplitude does not automatically determine wave speed. Wave speed depends on the properties of the medium and the type of wave. For example, wave speed on a stretched string depends on its tension and linear mass density.

2. Is amplitude the same as loudness or brightness?

No. Amplitude is a physical property of a wave. For sound, greater pressure amplitude generally corresponds to greater intensity and perceived loudness. For light, greater electromagnetic field amplitude corresponds to greater intensity and can result in greater brightness under comparable conditions.

3. Can amplitude change over time?

Yes. Amplitude can change over time, particularly in damped oscillations. Damping causes energy to be transferred to the surroundings, resulting in a gradual reduction in amplitude.

4. How do you find amplitude on a wave graph?

First identify the equilibrium line. Then measure the maximum vertical displacement from this line to a crest or trough. This distance is the amplitude.

5. Is amplitude half the distance between a crest and a trough?

Yes, for a wave with a symmetric displacement about its equilibrium position, the crest-to-trough distance is twice the amplitude. Therefore, amplitude is half this distance.

6. What is the relationship between amplitude and energy?

For many wave systems under appropriate conditions, energy transported is proportional to the square of amplitude. Therefore, doubling the amplitude makes the energy four times greater.

7. What is the difference between amplitude in transverse and longitudinal waves?

In a transverse wave, amplitude is the maximum displacement of particles perpendicular to the direction of wave travel. In a longitudinal wave, such as sound in air, amplitude can be described through the maximum pressure or density variation from equilibrium.

8. What are nodes and antinodes in standing waves?

Nodes are points in a standing wave that always have zero displacement. Antinodes are points where the maximum displacement is greatest. The amplitude is zero at nodes and maximum at antinodes.

9. What is damping in wave motion?

Damping is the gradual reduction in the amplitude of an oscillation due to energy transfer to the surroundings. Friction and resistance are common causes of damping.

10. Does a larger amplitude mean a higher frequency?

No. Amplitude and frequency describe different properties. Amplitude measures maximum displacement, while frequency measures the number of complete oscillations per second. Increasing amplitude does not necessarily increase frequency.

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