The **wave characteristics** They are the hallmarks of the wave phenomenon: the wavelength, the frequency, the valleys, the crests, the speed, the energy and others that we will explain in this article.

In waves, it is not particles that travel with the disturbance, but energy. When a wave propagates in a material medium, which can be water, air or a string, among others, the particles barely move from the equilibrium position, to return to it after a short time.

However, the movement is transmitted from one particle to another, making each of them vibrate. In this way, the disturbance that we call *vibe*just like the wave of fans does in the stadiums, when football matches are played.

The study of waves is very interesting, since we live in a world full of them: light, ocean waves, the sound of music and voice are all wave phenomena, although of a different nature. Both light and sound are particularly important, as we continually need them to communicate with the outside world.

**What are the characteristics of waves?**

**Vibration**

It is the complete path that a particle makes in its to-and-fro motion. For example, a pendulum swings, since starting from a certain point, it describes an arc, stops when it reaches a certain height and returns to its original position.

If it were not for friction, this movement would continue indefinitely. But because of the friction, the movement becomes slower and slower and the swing less wide, until the pendulum stops.

When a taut horizontal string is disturbed, the particles on the string vibrate in the vertical direction, that is, from top to bottom, while the disturbance travels horizontally along the string.

**swing center**

When a particle makes its to-and-fro movement, it does so by moving about a certain point, called the origin or center of oscillation.

In the pendulum example, it is in equilibrium at the lowest point, and it oscillates around it if we move it slightly away from this position. Therefore, this point can be considered the center of the oscillation.

We can also imagine a spring or spring on a horizontal table, attached to a wall at one end, and with a block at the other end. If the spring-block system is undisturbed, the block is in a certain equilibrium position.

However, by compressing or stretching the spring a bit, the system begins to oscillate around that equilibrium position.

**Elongation**

It is the distance that the particle moves away from the center of oscillation after a while. It is measured in meters when the International System SI is used.

If a spring with a block on one end is compressed or stretched, it is said to have experienced an elongation of “x” number of meters, centimeters, or whatever unit is being used to measure distance.

**ridges and valleys**

They are, respectively, the highest and lowest points that the particle reaches with respect to the equilibrium position y=0 (see figure 1).

**Amplitude**

It is the maximum distance that the particle separates from the center of oscillation and is also given in meters. It is denoted as *TO *or as *and*. There the equilibrium position coincides with y = 0 and corresponds to the crests and troughs of the wave.

The amplitude is an important parameter, since it is related to the energy that the wave carries. The greater the amplitude, the greater the energy, as is the case with ocean waves, for example.

**Node**

The nodes are the points at which the particle passes through the center of oscillation or equilibrium position.

**Cycle**

This is the name given to a complete oscillation, when the particle passes from one crest to the next, or from one trough to the next. So we say that it performed a cycle.

The pendulum completes a complete oscillation when it moves a certain height away from the equilibrium position, passes through the lowest point, rises to the same height on the outward trip, and returns to the initial height on the return trip.

**Period**

Since the waves are repetitive, the motion of the particles is periodic. The period is the time it takes to make one complete oscillation and is often denoted by the capital letter T. The units of the period in the SI International System are seconds (s).

**Frequency**

It is the inverse or reciprocal magnitude of the period and is related to the number of oscillations or cycles carried out per unit of time. It is denoted by the letter *F*.

As the number of oscillations is not a unit, seconds-1 (s-1) are used for the frequency, called Hertz or hertz and abbreviated Hz.

Being the inverse of the period, we can write a mathematical relationship between both magnitudes:

f = 1 /T

O well:

T = 1/f

If, for example, a pendulum executes 30 cycles in 6 seconds, its frequency is:

f = (30 cycles)/(6 s) = 5 cycles/s = 5 Hz.

**Wavelength**

It is the distance between two points of a wave that are at the same height, provided that a complete oscillation has been carried out. It can be measured from one peak to another consecutive one, for example, but also from valley to valley.

The wavelength is denoted by the Greek letter λ, which is read “lambda” and is measured in units of distance such as meters in the International System, although there is such a wide variety of wavelengths that multiples and submultiples are frequent. .

**wave number**

It is the inverse magnitude of the wavelength, multiplied by the number 2π. Therefore, denoting the wave number by the letter k, we have:

k = 2π / λ

**propagation speed**

It is the speed with which the disturbance travels. If the medium in which the wave propagates is homogeneous and isotropic, that is, its properties are the same everywhere, then this speed is constant and is given by:

v = λ / T

The units of the speed of propagation are the same as those of any other speed. In the International System it corresponds to am/s.

Since the period is the inverse of the frequency, it can also be expressed:

v = λ. F

And since the speed is constant, so is the product λ.f, so that if, for example, the wavelength is changed, the frequency changes so that the product remains the same.

**References**

Giancoli, D. 2006. Physics: Principles with Applications. 6th. Ed Prentice Hall.

Hewitt, Paul. 2012. Conceptual Physical Science. 5th. Ed. Pearson.

Sears, Zemansky. 2016. University Physics with Modern Physics. 14th. Ed. Volume 1. Pearson.

Serway, R., Jewett, J. (2008). Physics for Science and Engineering. Volume 1.7ma. Ed. Cengage Learning.

Tipler, P. (2006) Physics for Science and Technology. 5th Ed. Volume 1. Editorial Reverté.