Wave Characteristics with Examples

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 rope, among others, the particles hardly move from the equilibrium position, to return to it after a short time. Wave Characteristics

However, the movement is transmitted from one particle to another, causing each of them to vibrate. In this way, the disturbance we call wave spreads in the middle , just as the wave of fans does in stadiums when football matches are played.

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

What are the characteristics of the waves?

Vibration

It is the complete path that a particle makes in its back and forth motion. For example, a pendulum has a back and forth movement, since when it starts from a certain point, it describes an arc, stops when it reaches a certain height and returns to its original position.

If it weren’t for friction, this movement would continue indefinitely. But because of friction, the movement becomes slower and slower and the oscillation less wide, until the pendulum stops. Wave Characteristics

When a horizontal taut string is disturbed, the particles in 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 back and forth motion, it does so by moving about a certain point, called the origin or center of oscillation.

In the example of the pendulum, it is in equilibrium at the lowest point, and it oscillates around it if we separate it a little from this position. Therefore this point can be considered the center of the oscillation.We can also imagine a spring on a horizontal table, attached at one end to a wall, 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 time. It is measured in meters when the SI International System is used.

If a spring with a block at 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 A or as y . There the equilibrium position coincides with y = 0 and corresponds to the peaks and valleys of the wave.

Amplitude is an important parameter, as it is related to the energy carried by the wave. The greater the amplitude, the greater the energy, as with ocean waves, for example.

Node Wave Characteristics

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

Cycle Wave Characteristics

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

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

Period Wave Characteristics

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

Frequency Wave Characteristics

It is the inverse or reciprocal magnitude of the period and is related to the number of oscillations or cycles performed per unit of time. It is denoted by the letter f .

As the amount of oscillations is not a unit, for the frequency the seconds ^-1 (s ^-1 ) are used, 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 Wave Characteristics

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

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 great variety of wavelengths that multiples and submultiples are frequent .

Wave number Wave Characteristics

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

k = 2π / λ

Velocity of propagation Wave Characteristics

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 for velocity of propagation are the same as for any other velocity. In the International System it corresponds to m / s.

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

v = λ. F

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