Crest (physics): the peak point of a wave

Key characteristics

Several measurable quantities relate to crests and troughs: amplitude (the magnitude of displacement from the equilibrium), wavelength (distance between successive crests), and period or frequency (time or cycles per second). A single repetitive unit is called a cycle; the crest marks the point of greatest positive displacement in that cycle — see cycle. The lowest point in the same cycle is the trough.

Interference and phase

When two or more waves overlap, the resulting displacement follows the superposition principle. If crests from separate sources arrive in step (that is, they are in phase), their amplitudes add and produce a larger crest — known as constructive interference. If one wave's crest aligns with another's trough (approximately 180° out of phase), they cancel and may produce little or no net displacement, a situation called destructive interference. In ideal complete cancellation the result is the undisturbed equilibrium with zero amplitude.

Examples and applications

• Water waves: crests are the visible peaks on the surface; crest height matters for navigation and coastal engineering.
• Sound waves: pressure crests correspond to regions of higher air pressure; their amplitude relates to loudness.
• Electromagnetic waves: crests refer to maxima of electric or magnetic field components in the oscillation.

Measurement, representation and notable facts

Crests are commonly shown on graphs of displacement versus time or distance, and are naturally represented by sine or cosine functions in linear wave theory. Standing waves exhibit fixed crests (antinodes) and nodes where displacement is always zero. In many practical contexts — from musical instruments to antenna design and ocean forecasting — tracking crest positions and amplitudes is essential. Note that in nonlinear or breaking waves, the simple crest/trough picture becomes more complex and requires detailed modelling.