AP Syllabus focus: 'Amplitude is the maximum displacement from equilibrium. In longitudinal pressure waves, amplitude may be measured by pressure change; sound loudness and wave energy increase with amplitude.'
Amplitude tells us how large a wave disturbance is. In AP Physics 2, it is especially important for describing sound, comparing wave strength, and reasoning about energy transfer.
Amplitude
What amplitude measures
When a wave passes through a medium, points in the medium move away from their normal positions and then return. The size of that motion is described by amplitude.
Amplitude: The maximum displacement of a point in a wave from its equilibrium position.
The phrase maximum displacement is essential. Amplitude is measured from the equilibrium position to one extreme value, not from the highest point of the wave to the lowest point. If a point moves 2 cm above equilibrium and 2 cm below equilibrium, the amplitude is 2 cm.
For any wave, a larger amplitude means a larger disturbance of the medium or field being represented. In a transverse wave, that disturbance is often shown as a greater upward, downward, or sideways displacement. Amplitude therefore tells you how strong the disturbance is. It does not tell you how fast the wave travels.
Equilibrium and displacement
The equilibrium position is the undisturbed state of the medium before the wave passes through it. Amplitude is always measured relative to that reference level. This is why good diagrams usually include a midline or rest position.
This OpenStax textbook figure shows a physical wave with the equilibrium position drawn as a dotted reference line and the amplitude defined as the maximum displacement from that line. It helps students transfer the idea of “measured from equilibrium” from idealized graphs to real wave motion in a medium. Source
A common error is to confuse amplitude with the total vertical height of a wave picture.
The full crest-to-trough height is twice the amplitude. On graphs, always identify the equilibrium line first, and then measure the maximum departure from that line.
Amplitude in sound waves
Pressure change as amplitude
For sound waves, amplitude is often described differently because sound is modeled as a longitudinal pressure wave. Instead of large visible displacements like a string moving up and down, sound is usually represented by changing pressure in the medium.
As a sound wave travels through air, the air pressure oscillates about its normal value.
At some locations the pressure is slightly above the average value, and at others it is slightly below. In this case, the amplitude can be described by the size of the pressure change from equilibrium pressure.
That means amplitude does not always have units of distance. For sound, it may be measured using a pressure difference instead. The key idea is the same in either case: amplitude tells you how far the wave variable moves away from equilibrium.
A larger pressure variation means a larger-amplitude sound wave. A smaller pressure variation means a smaller-amplitude sound wave.
Loudness and amplitude
When discussing sound, loudness refers to how strong a sound is perceived to be by a listener.
Loudness: The perceived strength of a sound; in general, sound waves with greater amplitude are heard as louder.
For AP Physics 2, the main relationship is qualitative: as amplitude increases, loudness increases. If one sound wave produces larger pressure changes in the air than another, it is generally heard as louder.
This relationship is physical, not just graphical. Larger-amplitude sound waves create larger oscillations in air pressure at the ear. Because the disturbance is greater, the sound is typically perceived as stronger.
On comparison questions, this idea is often enough to answer correctly. If two sound waves are shown and one has the greater amplitude, that one is expected to be louder.
Wave energy and amplitude
Waves transfer energy from one location to another. The syllabus emphasizes that wave energy increases with amplitude. A larger-amplitude wave carries more energy than a smaller-amplitude wave of the same kind in the same situation.
This makes sense physically. Creating a larger disturbance requires more energy, and the resulting wave can transfer more energy as it travels. For sound, larger pressure changes mean the medium is being disturbed more strongly, so more energy is associated with the wave.
For qualitative AP reasoning, keep these comparisons in mind:
larger amplitude means more wave energy
smaller amplitude means less wave energy
for sound, larger amplitude means greater loudness
You do not need a detailed mathematical treatment here to use the idea correctly. The important point is the direction of the relationship: amplitude goes up, loudness and wave energy go up.
Reading graphs and diagrams
Amplitude may appear on different kinds of graphs, but the meaning stays consistent.
On a displacement graph, amplitude is the maximum displacement from equilibrium.
On a pressure graph for sound, amplitude is the maximum pressure change from equilibrium pressure.
On any graph, amplitude is measured from the midline or equilibrium line to one extreme.
Be careful with visual representations. A graph with taller peaks does not just look larger; it represents a larger oscillation. That larger oscillation corresponds to a larger amplitude, which in this subtopic means a louder sound and greater wave energy when the wave is sound.
FAQ
Loudness is a human perception, not a direct one-to-one physical measurement. The ear and brain respond nonlinearly, so a simple change in amplitude does not produce an equally simple change in what a listener experiences.
That is why a sound with greater amplitude is louder in general, but not necessarily “twice as loud” in any exact everyday sense.
As sound spreads out, the disturbance reaching the listener becomes weaker. That usually means the pressure variations at the listener are smaller than they were closer to the source.
So even if the source creates the same original sound, the amplitude at your position can be reduced, making the sound seem quieter.
The range of audible sounds is extremely large, so raw amplitude values can be inconvenient to compare. A decibel scale compresses that huge range into a more manageable form.
It is also useful because human hearing does not respond in a simple linear way, so decibels often give a more practical description of sound level.
Yes. In many sound waves, the actual particle motion is very small, but the wave still transfers energy through organized pressure oscillations in the medium.
Because enormous numbers of particles participate, even small individual motions can add up to a significant transfer of energy.
A microphone converts pressure variations in air into an electrical signal. Larger pressure changes push or deform the sensing part of the microphone more strongly.
That means a larger-amplitude sound wave usually produces a larger electrical signal, which is why microphones are useful for detecting changes in loudness.
Practice Questions
Two sound waves in air are measured at the same location. Wave A causes a larger maximum pressure change than Wave B.
State: (a) which wave has the greater amplitude (b) which wave is expected to sound louder
1 mark: Wave A has the greater amplitude.
1 mark: Wave A is expected to sound louder.
A microphone records two sound signals from different speakers. Signal X has a smaller maximum pressure variation from equilibrium than Signal Y.
(a) Which signal corresponds to the larger-amplitude sound wave?
(b) Which sound wave carries more energy?
(c) Explain why amplitude for a sound wave can be described using pressure change.
(d) A student says the amplitude is the vertical distance from the highest pressure point to the lowest pressure point on the graph. Explain the mistake.
1 mark: Signal Y has the larger amplitude.
1 mark: Signal Y carries more energy.
1 mark: Sound is a longitudinal pressure wave, so amplitude can be measured by the maximum pressure change from equilibrium pressure.
1 mark: Amplitude must be measured from equilibrium to one extreme.
1 mark: The student used the full peak-to-trough change, which is twice the amplitude.
