The amplitude of a wave is the maximum displacement of the wave from its resting position. Think of a rope lying flat on the ground: if you flick one end, the rope rises to a peak and dips to a trough. The height of that peak, measured from the rope’s original flat position, is the amplitude. This single measurement tells you how much energy the wave carries, whether it’s a sound wave, a light wave, an ocean swell, or a vibration through the earth.
How Amplitude Is Measured
Every wave oscillates around a central resting point called the equilibrium position. Amplitude is the distance from that equilibrium to the farthest point the wave reaches, either up to the peak or down to the trough. In a perfectly symmetrical wave, those two distances are equal, so it doesn’t matter which direction you measure.
For a wave on a string, amplitude is literally how far the string moves above or below its undisturbed position. For a sound wave, it’s how much the air pressure rises above or drops below normal atmospheric pressure. For a light wave, it’s the strength of the oscillating electric and magnetic fields. The physical thing being displaced changes depending on the type of wave, but the concept is always the same: maximum displacement from rest.
Transverse vs. Longitudinal Waves
In a transverse wave, the material moves perpendicular to the wave’s travel direction. Picture shaking one end of a slinky side to side while it stretches across a table. The coils move left and right, but the wave pulse travels along the length of the slinky. Amplitude here is the sideways distance from the resting line to the farthest point of displacement.
In a longitudinal wave, the material moves parallel to the wave’s travel direction. Push and pull one end of that same slinky along its length, and you create regions where coils bunch together (compressions) and spread apart (rarefactions). Amplitude in this case is the maximum distance a coil shifts forward or backward from its equilibrium spot. Sound waves work this way: air molecules compress and expand along the direction the sound travels, and the pressure amplitude determines how loud the sound is.
Amplitude in the Wave Equation
The standard equation for a wave on a string looks like this: y(x, t) = A sin(kx − ωt). The variable A is the amplitude. It controls the vertical scaling of the sine wave. Since a plain sine function oscillates between +1 and −1, multiplying by A means the wave oscillates between +A and −A. You can read amplitude directly from this equation without any further calculation.
The other variables describe different properties. The wave number (k) relates to wavelength, and the angular frequency (ω) relates to period and frequency. But amplitude stands alone: it has nothing to do with how fast the wave moves or how tightly the peaks are spaced. A wave can have a long wavelength and a tiny amplitude, or a short wavelength and a huge amplitude. These are independent properties.
Peak, Peak-to-Peak, and RMS Amplitude
Engineers and technicians use several variations of amplitude depending on the application:
- Peak amplitude (also called zero-to-peak) is the standard definition: the maximum deviation from the resting level to either the highest or lowest point of the wave.
- Peak-to-peak amplitude is the total vertical distance from the lowest trough to the highest crest. For a symmetrical wave, this is exactly twice the peak amplitude. It’s useful when you need to know the total range of motion, such as measuring shaft displacement in machinery.
- RMS amplitude (root mean square) is a kind of average that accounts for the fact that a wave spends most of its time at values less than its peak. For a simple sine wave, RMS amplitude is about 0.707 times the peak amplitude. Electrical engineers use RMS values constantly because they represent the effective, continuous energy delivery of an alternating signal.
When someone says “amplitude” without specifying, they almost always mean peak amplitude.
Amplitude and Energy
Amplitude is directly tied to how much energy a wave carries, but the relationship isn’t one-to-one. A wave’s energy is proportional to the square of its amplitude. Double the amplitude, and the energy increases by a factor of four. Triple it, and energy goes up by a factor of nine. This square relationship has real consequences: a sound wave with twice the pressure amplitude delivers four times the energy to your eardrums.
This is why small increases in amplitude can translate to dramatic differences in power. It also explains why intensity, the amount of energy a wave delivers per unit area, scales with amplitude squared. Two identical waves that combine perfectly in phase produce a wave with twice the amplitude but four times the intensity of either wave alone.
Amplitude in Sound
For sound waves, amplitude corresponds to the pressure fluctuation in the air, and we perceive it as loudness. The scale used to quantify this is the decibel scale for Sound Pressure Level (SPL). The reference point, 0 dB, is set at a pressure amplitude of 0.00002 newtons per square meter, roughly the quietest sound a human ear can detect. The threshold of pain, around 120 dB, corresponds to a pressure amplitude of 20 newtons per square meter, a millionfold increase.
Because the decibel scale is logarithmic, every 6 dB increase represents a doubling of the pressure amplitude. A sound at 56 dB has twice the pressure amplitude of a sound at 50 dB. This logarithmic compression makes the scale practical: it compresses an enormous range of physical amplitudes into a manageable set of numbers that roughly tracks how our ears perceive changes in loudness.
Amplitude in Light
For electromagnetic waves like visible light, amplitude determines brightness. A light wave with a larger amplitude appears more intense and the color looks more vivid. A dim red light and a brilliant red light have the same wavelength (which determines the color), but the brilliant one has a greater amplitude. This holds across the electromagnetic spectrum: radio towers broadcast stronger signals by increasing the amplitude of their radio waves, not by changing the frequency.
Amplitude in Earthquakes
Seismic waves, the vibrations that travel through the earth during an earthquake, are measured by seismographs that record ground displacement over time. The Richter magnitude scale is built directly on amplitude: each whole number increase in magnitude represents a tenfold increase in the measured wave amplitude on a seismogram. A magnitude 6 earthquake produces seismic waves with 10 times the amplitude of a magnitude 5, and 100 times the amplitude of a magnitude 4. Because energy scales with amplitude squared (and additional geometric factors), each magnitude step actually represents about 31.6 times more energy released.
Amplitude in Ocean Waves
Oceanographers distinguish between wave height and wave amplitude. Wave amplitude is the vertical distance from the undisturbed sea surface to the crest (or trough) of a wave. Wave height is the full vertical distance from trough to crest, making it equivalent to peak-to-peak amplitude. A wave with a 2-meter amplitude has a 4-meter wave height.
Maritime forecasts typically report wave height rather than amplitude because it gives a more intuitive sense of what a ship or swimmer will experience. The commonly referenced “significant wave height” used in forecasts is defined as four times the RMS of the sea surface elevation, which closely approximates the average height of the tallest one-third of waves. This statistical measure smooths out the chaotic reality of open ocean swells into a single useful number.