A wave is a disturbance that travels through a medium or space, transferring energy from one location to another without transporting matter itself. For instance, a water wave moves across the ocean surface, but the water molecules only oscillate up and down around their original position. Understanding the anatomy of this disturbance is fundamental in physics, providing the language necessary to describe how light, sound, and ocean swells move.
The Crest and the Trough
The peak of a wave, which is the highest point of positive displacement from the wave’s equilibrium position, is known as the crest. This term applies specifically to transverse waves, such as ocean waves or electromagnetic waves like light, where the medium’s particles move perpendicular to the direction the energy is traveling.
Conversely, the lowest point of the wave’s cycle, representing the maximum negative displacement from the equilibrium line, is called the trough. The trough is the valley that follows the peak. The interaction between the crests and troughs of two different waves determines if they will combine to create a larger wave or cancel each other out.
Measuring Wave Size: Amplitude and Wavelength
The characteristics of the crest and trough allow for the measurement of two fundamental properties: amplitude and wavelength.
Amplitude is the measure of the wave’s height, defined as the maximum displacement from the equilibrium position to either the crest or the trough. This measurement is directly related to the amount of energy a wave carries; a larger amplitude signifies a more energetic wave. For example, the massive ground displacement seen in a major earthquake wave indicates its high amplitude.
Wavelength, symbolized by the Greek letter lambda, is the horizontal distance that a full wave cycle occupies. It is measured as the distance between two consecutive crests or two consecutive troughs. Wavelength, along with frequency (the number of cycles passing a point per second), determines the wave’s propagation speed through a given medium. Wave speed equals the wavelength multiplied by the frequency.
Waves That Don’t Have a Crest
Not all waves exhibit the characteristic peaks and valleys of crests and troughs. This visual terminology is not applicable to longitudinal waves, where the movement of the medium’s particles is parallel to the direction of energy transfer. Sound waves traveling through air are a common example of this type of wave.
Instead of crests and troughs, longitudinal waves are described by areas of varying density and pressure. The equivalent of a crest in a longitudinal wave is a compression, which is a region where the particles of the medium are tightly packed together, resulting in higher density and pressure. The counterpart to the trough is the rarefaction, an area where the particles are spread furthest apart, creating a region of lower density and pressure. The distance separating the centers of two consecutive compressions defines the wavelength for a longitudinal wave.