Amplitude is a measure of the maximum magnitude of an oscillating quantity relative to its equilibrium, reference, or mean value. In a simple sinusoidal wave, amplitude is the maximum displacement from the equilibrium position. It is commonly represented by the letter A. For a wave on a string, amplitude can be the maximum vertical displacement of the string from its rest position.
For a sound wave, amplitude can refer to the magnitude of pressure variation or particle displacement, depending on the quantity being measured. For an electromagnetic wave, amplitude can refer to the maximum electric or magnetic field strength. Amplitude therefore does not have one universal physical unit because its units depend on what quantity is oscillating. Unlike wavelength and frequency, amplitude describes the size or strength of the oscillation rather than its spatial period or rate of repetition.
In a sinusoidal wave, the amplitude is the distance from the equilibrium line to a crest or trough in a transverse displacement graph. The total crest to trough height is twice the amplitude, not the amplitude itself. This distinction is important when reading wave diagrams and experimental data.
If the maximum displacement is 0.04 metres above equilibrium and the minimum displacement is 0.04 metres below equilibrium, the amplitude is 0.04 metres and the total peak to peak displacement is 0.08 metres. For quantities that can take positive and negative values, amplitude is normally treated as a positive magnitude even though the instantaneous displacement can have either sign. In more complicated waves, especially nonsinusoidal signals, several definitions may be used, including peak amplitude, peak to peak amplitude, root mean square amplitude, and envelope amplitude. These definitions serve different measurement purposes and should not be treated as identical.
Amplitude is closely connected to wave energy, but the exact relationship depends on the physical type of wave. For many linear mechanical waves, the average energy carried by the wave is proportional to the square of its amplitude. Consequently, doubling the amplitude can produce approximately four times the energy under conditions where the relevant assumptions remain valid.
For electromagnetic radiation, intensity is proportional to the square of the electric field amplitude in classical descriptions, while photon energy depends on frequency rather than directly on classical field amplitude. In acoustics, sound intensity is related to pressure amplitude squared under appropriate conditions, and sound level is commonly expressed logarithmically in decibels. These relationships explain why amplitude is often associated with the strength or intensity of a wave, but they also show why amplitude alone is not a universal measure of energy. The precise physical quantity whose amplitude is being measured must always be specified.
Amplitude can change as a wave propagates. In an ideal lossless system, a travelling wave may maintain its amplitude, but real systems commonly involve attenuation caused by absorption, scattering, geometric spreading, friction, viscosity, electrical resistance, or other energy transfer mechanisms. A spherical wave spreading from a point source distributes energy over an increasingly large area, so the intensity generally decreases with distance even if the medium itself does not strongly absorb the wave.
In materials, energy can be converted into heat or other forms, reducing the wave amplitude. Amplification can occur when energy is supplied to a wave or oscillator, while feedback systems can either increase or decrease amplitude depending on their design. Measuring amplitude as a function of distance can therefore provide information about material properties, energy losses, source strength, and propagation conditions.
Amplitude is particularly important in oscillators and resonance. A driven oscillator can experience a large increase in amplitude when the driving frequency approaches a natural frequency, depending on damping and other system properties. The resulting amplitude response is used to characterise mechanical structures, electrical circuits, acoustic systems, and optical devices. Damping limits the growth of amplitude by dissipating energy, and the degree of damping affects both the maximum response and the width of the resonance curve.
In engineering, controlling amplitude can be essential for preventing excessive vibration and structural damage. In communications, amplitude can deliberately carry information through amplitude modulation or other signalling methods. In audio systems, amplifier gain controls signal amplitude, while excessive amplitude can cause clipping and distortion. Thus amplitude can be both a physical consequence of a wave and a quantity deliberately manipulated for technological purposes.
Amplitude must be distinguished from frequency and wavelength because these quantities describe different characteristics. Two waves can have identical frequency and wavelength but different amplitudes, meaning they repeat at the same rate and travel with the same spatial spacing but differ in oscillation magnitude. Conversely, two waves can have the same amplitude but different frequencies or wavelengths. Increasing amplitude does not normally change the frequency of an ideal linear oscillator, although nonlinear systems can behave differently.
Similarly, increasing amplitude does not necessarily change wave speed in a linear medium, but in nonlinear media the propagation speed can depend on amplitude. This distinction is particularly important when interpreting diagrams because a visually larger wave is not necessarily travelling faster or having a longer wavelength. Graphical scale can also be misleading if axes are not labelled with physical units.
Different fields use amplitude terminology in specialised ways. In signal processing, peak amplitude describes the largest excursion from a reference level, while peak to peak amplitude measures the difference between maximum and minimum values. Root mean square amplitude is useful for alternating electrical signals because it relates to equivalent power under appropriate conditions. In acoustics, pressure amplitude can describe fluctuations around atmospheric pressure.
In optics, field amplitude relates to electromagnetic field strength, while optical intensity relates to the square of the field amplitude for a coherent classical field. In quantum mechanics, the term amplitude can refer to probability amplitude, which is a complex quantity and should not be interpreted as a classical physical displacement. The probability associated with a quantum state is related to the modulus squared of its probability amplitude. This demonstrates that the word amplitude can have a technical meaning that depends strongly on the theoretical framework.
Amplitude has major practical significance because it often indicates the magnitude of a measurable physical response. Seismologists use seismic wave amplitudes when analysing earthquake signals and estimating source characteristics, although interpretation requires consideration of distance, frequency, attenuation, instrument response, and geological structure. Engineers monitor vibration amplitudes to identify faults, resonance, imbalance, or structural problems. Medical ultrasound systems use controlled acoustic amplitudes to produce images and, in some applications, therapeutic effects, while safety limits constrain exposure.
Radio receivers measure signal amplitudes to determine signal strength, and sensors convert physical quantities into electrical signals whose amplitudes can be analysed. A correct interpretation of amplitude therefore requires identifying the underlying oscillating quantity, its reference level, its units, the measurement method, and the physical relationship between amplitude and energy or intensity in that particular system.
