Study Material

# Wave motion: examples, characteristics, and types of waves

We explain the wave motion: characteristics, types of waves, examples. The wave motion is the propagation of a disturbance, called wave in a material or even in the vacuum environment, whether it is light or other electromagnetic radiation.

The energy travels in wave motion, without the particles in the medium moving too far from their positions, since the disturbance only makes them oscillate or vibrate continuously around the equilibrium site. examples of wave motion

And this vibration is what is transmitted from one particle to another in the middle, in what is known as aÂ mechanical waveÂ .Â Sound propagates in this way: a source alternately compresses and expands the air molecules, and the energy that travels in this way is in turn responsible for setting the eardrum to vibrate, a sensation that the brain interprets as sound.

In the case of light, which does not need a material medium, it is the oscillation of electric and magnetic fields that is transmitted.

As we can see, two of the most important phenomena for life: light and sound, have wave motion, hence the importance of knowing more about their behavior.

## Characteristics of wave motion

Waves have several characteristic attributes that we can group according to their nature:

• Spatial characteristics, which refer to the shape.
• Temporal or duration characteristics.

Let’s look at a schematic representation of a simple wave as a periodic succession of peaks and valleys.Â The drawing represents little more than a cycle or what is the same: a complete oscillation.

### Spatial characteristics of waves

These elements are common to all waves, including light and sound.

• CrestÂ : the highest position.
• ValleyÂ : the lowest.
• NodeÂ : point where the wave intersects at the equilibrium position.Â In the figure it is the segmented line or horizontal axis.
• WavelengthÂ : denoted with the Greek letter Î» (lambda) is the distance between two successive crests, or between one point and another that has the same height, but of the next cycle.
• ElongationÂ : it is the vertical distance between a point of the wave and the equilibrium position.
• AmplitudeÂ : it is the maximum elongation.

### Temporal characteristics of waves

• PeriodÂ , the time that a complete cycle lasts.
• FrequencyÂ : number of waves produced per unit of time.Â It is the inverse or reciprocal of the period.
• SpeedÂ : it is defined as the quotient between the wavelength and the period.Â If denoted as v, in mathematical form this relationship is:

v = Î» / T

## Types of waves

There are different types of waves, since they are classified according to several criteria, for example they can be classified according to:

• The direction the disturbance is leading.
• The medium in which they spread.
• The direction in which the particles in the medium oscillate.

A wave can be of several types at the same time, as we will see below:

### – Waves according to the oscillation of the medium

The particles that make up the medium have the ability to respond in various ways to the disturbance, in this way they arise:

#### Transverse waves

The medium particles oscillate in a direction perpendicular to that of the disturbance.Â For example, if we have a horizontal taut string that is disturbed at one end, the particles oscillate up and down, while the disturbance travels horizontally.

Electromagnetic waves also travel in this way, whether they do so in a material medium or not.

#### Longitudinal waves

Propagation travels in the same direction as the particles in the medium.Â The best-known example is sound, in which the noise disturbance compresses and expands the air as it moves through it, causing the molecules to move back and forth.

### – Waves according to the medium in which they propagate

#### Mechanical waves

They always require a material medium to propagate, which can be solid, liquid or gas.Â Sound is also an example of a mechanical wave, as well as the waves that are produced in the taut strings of musical instruments and those that propagate around the globe: seismic waves.

#### Electromagnetic waves

Electromagnetic waves can propagate in a vacuum.Â There are no oscillating particles, but electric and magnetic fields that are mutually perpendicular, and at the same time perpendicular to the direction of propagation.

The spectrum of electromagnetic frequencies is very wide, but we hardly perceive with our senses a narrow band of wavelengths: the visible spectrum. examples of wave motion

### Waves according to the direction of propagation

Depending on the direction of propagation, the waves can be:

• One-dimensional
• Two-dimensional
• Three-dimensional

If we have a taut string, the disturbance travels the entire length, that is, in one dimension.Â It also occurs when a flexible spring or spring likeÂ slinkyÂ is disturbedÂ .

But there are waves that move on a surface, such as the surface of water when a stone is thrown into a pond or those that propagate in the earth’s crust, in this case we speak of two-dimensional waves.

Finally, there are waves continually traveling in all directions in space like sound and light.

### -Waves according to their extension

Waves can travel over large areas, such as light waves, sound, and seismic waves.Â Instead others are limited to a smaller region.Â That is why they are also classified as:

-Traveling waves

-Standing waves.

#### Traveling waves

When a wave propagates from its source and does not return to it, you have a traveling wave.Â Thanks to them weÂ heard the sound of music coming from a neighboring room and reaches the light of theÂ sunÂ , which must travel 150 million kilometers into space to illuminate the planet.Â It does so at a constant speed of 300,000 km / s.

#### Standing waves

Unlike traveling waves, standing waves move in a limited region, for example disturbance in the string of a musical instrument such as a guitar. examples of wave motion

#### Harmonic waves

Harmonic waves are characterized by being cyclical or periodic.Â This means that the disturbance repeats every certain constant time interval, calledÂ the waveÂ periodÂ .

Harmonic waves can be mathematically modeled using the sine and cosine functions. examples of wave motion

#### Non-periodic waves

If the disturbance does not repeat every certain time interval, the wave is not harmonic and its mathematical modeling is much more complex than that of harmonic waves.

## Examples of wave motion

Nature presents us with examples of wave motion all the time, sometimes this is obvious, but sometimes not, as in the case of light: how do we know that it moves like a wave?

The wave nature of light was debated for centuries.Â Thus, Newton was convinced that light was a flow of particles, while Thomas Young, at the beginning of the 19th century, showed that it behaved like a wave.

Finally, one hundred years later Einstein affirmed, to everyone’s peace of mind, that light was dual: wave and particle at the same time, depending on whether its propagation or the way in which it interacts withÂ matterÂ is studiedÂ .

By the way, the same thing happens with the electrons in the atom, they are also dual entities. They are particles, but they also experience phenomena unique to waves, such as diffraction, for example. examples of wave motion

Let’s now look at some everyday examples of obvious wave motion:

### The pier examples of wave motion

A soft spring, spring orÂ slinkyÂ consists of a helical spring with which longitudinal and transverse waves can be visualized, depending on the way in which it is disturbed by one of its ends.

### The strings of musical instruments

When you press an instrument such as a guitar or harp, you observe the standing waves going back and forth between the ends of the string.Â The sound of the string depends on its thickness and the tension to which it is subjected.

The tighter the string, the more easily a disturbance propagates through it, just as when the string is thinner.Â It can be shown that the square of the velocity of the wave vÂ 2Â is given by:

vÂ 2Â = T / Î¼

Where T is the tension in the string and Î¼ is itsÂ linearÂ densityÂ , that is, its mass per unit length.

### The voice examples of wave motion

We have the vocal cords, with which sounds are emitted for communication.Â Its vibration is perceived by placing the fingers on the throat when speaking.

### Sea waves examples of wave motion

They propagate in oceanic bodies at the boundary between water and air, and are originated by winds, which cause small portions of liquid to move back and forth.

These swings are amplified by the action of various forces in addition to the wind: friction, surface tension in the liquid, and the ever-present force of gravity.

### Seismic waves

The Earth is not a static body, since disturbances occur inside it that travel through the different layers.Â They are perceived as tremors and occasionally, when they carry a lot of energy, as earthquakes capable of causing a lot of damage.

### The structure of the atom

Modern atomic theories explain the structure of the atom by an analogy with standing waves. examples of wave motion

## Solved exercises

### Exercise 1

A sound wave has a wavelength equal to 2 cm and propagates at a rate of 40 cm in 10 s.

Calculate:

a) Its speed

a) The period

b) Frequency

#### Solution to

We can calculate the speed of the wave with the data provided, since it propagates at a rate of 40 cm in 10 s, therefore:

v = 40 cm / 10 s = 4 cm / s

#### Solution b

Previously, the relationship between speed, wavelength and period had been established as:

v = Î» / T

Therefore the period is:

T = Î» / v = 2 cm / 4 cm / s = 0.5 s.

#### Solution c

Since the frequency is the inverse of the period:

f = 1 / T = 1 / 0.5 s = 2 sÂ -1

The inverse of a second osÂ -1Â is called Hertz or hertz and is abbreviated Hz. It was given in honor of the German physicist Heinrich Hertz (1857-1894), who discovered how to produce electromagnetic waves.

### Exercise 2 examples of wave motion

A string is stretched under the action of a 125 N force. If its linear density Î¼ is 0.0250 kg / m, what will be the velocity of propagation of a wave?

#### Solution examples of wave motion

Previously we had seen that the speed depends on the tension and the linear density of the rope as:

vÂ 2Â = T / Î¼

Therefore:

vÂ 2Â = 125 N / 0.0250 kg / m = 5000 (m / s)Â 2

Taking the square root of this result:

v = 70.7 m / s

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