Waves (Properties & Characteristics): Amplitude, Period, Frequency, Wavelength

Wave motion is everywhere on Earth and in the universe. Types of waves include sound waves, water waves, waves on a string and electromagnetic waves, to name a few.

A wave, in technical terms, is a disturbance in a medium that propagates from one place to another via oscillations (back and forth motions) in that medium. More simply put, ​it is a vibration carried by matter through time and space​.

An important characteristic of a wave is that it ​transfers energy​ but not matter. A wave starts with an energy gain somewhere in a medium, such as a hand pushing on the surface of a pond. As each particle of a material receives energy from that initial push – in this example, the water molecules – it bumps into the particles next to it, which bump the next ones and so on.

The water molecules didn't all rearrange into new places in the pond; they only jostled back and forth against one another the way people standing shoulder-to-shoulder in a crowd might ricochet in place after someone at the edge falls into them.

Waves come in two types:

​Transverse waves​ are formed by matter that oscillates at right angles to the direction of the energy's motion. For instance, someone pumping the end of a jump rope fixed to a wall is moving the pieces of the medium (the rope) vertically while the energy travels horizontally along the rope to the wall, until the whole rope is moving.

​Longitudinal waves​ are formed by matter that oscillates in the same direction as the energy it carries. The earlier examples of ripples in a pool, or through a crowd that has been disturbed at one end are both longitudinal.

The most basic wave properties are wavelength, amplitude, frequency and period.

One ​wavelength​ is defined as the distance between any point on a wave ​to the exact same point on the next wave​​.​ For instance, one wavelength can be measured from the crest, or top, of a wave in the ocean to the crest of the next wave. Wavelength is denoted by the lowercase Greek letter lambda (​λ​) and uses the SI unit of length, meters (m).

The ​amplitude​ of the wave, ​A​, is a measure of the maximum displacement of any matter in the medium from is equilibrium (or rest position). So for a sine curve-shaped wave going up and down around the x-axis, the amplitude has the ​same magnitude as the highest or lowest position​. As a measure of displacement, amplitude is also measured in meters (m).

The ​frequency​ of a wave, ​f​, is a measure of how many waves pass by, or how many oscillations occur, in one second. The SI unit of frequency is hertz (Hz). For example, a child on a swing is oscillating back and forth around the swing's rest position, making one complete back-and-forth trip every three seconds. That means she goes through ​one-third of a full wave (oscillation) each second​, so her frequency would be 1/3 Hz.

The ​period​ of a wave, ​T​, is the inverse of the frequency; instead of how many waves per second, it measures the time for one full wave or oscillation to occur. Thus it is measured in the SI unit of time, seconds (s). For the same child on the swing, her wave period is three seconds. (Note that three is the inverse of one-third.)

Wave speed (​v​) is the rate at which a disturbance travels from one location to another. A wave travels at a speed (in meters per second, m/s) equal to the product of frequency and wavelength. The wave equation is therefore:

\(v=\lambda f\)