The wave motion It consists of the propagation of a disturbance, called a wave, in a material medium or even in a vacuum, if it is light or any 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..
And this vibration is the one that is transmitted from one particle to another in the middle, in what is known as a mechanical wave. 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..
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Waves have several characteristic attributes that we can group according to their nature:
Let's look at a schematic representation of a simple wave as a periodic succession of peaks and valleys. The drawing represents little more than a cycle or what is the same: a complete oscillation.
These elements are common to all waves, including light and sound..
v = λ / T
There are different types of waves, since they are classified according to several criteria, for example they can be classified according to:
A wave can be of several types at the same time, as we will see below:
The particles that make up the medium have the ability to respond in various ways to disturbance, in this way they arise:
The particles in the medium oscillate in a direction perpendicular to that of the disturbance. 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..
Propagation travels in the same direction as the particles in the medium. 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..
They always require a material medium to propagate, which can be solid, liquid or gas. 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 can propagate in a vacuum. 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.
Depending on the direction of propagation, the waves can be:
If we have a taut string, the disturbance travels the entire length, that is, in one dimension. It also occurs when a spring or flexible spring such as the slinky.
But there are waves that move on a surface, such as the surface of the water when a stone is thrown on 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 of space like sound and light..
Waves can travel over large areas, such as light waves, sound, and seismic waves. Instead others are limited to a smaller region. That is why they are also classified as:
-Traveling waves
-Standing waves.
When a wave propagates from its source and does not return to it, you have a traveling wave. Thanks to them we hear the sound of music that comes from a neighboring room and the sunlight reaches us, which must travel 150 million kilometers in space to illuminate the planet. It does so at a constant speed of 300,000 km / s.
Unlike traveling waves, standing waves move in a limited region, for example disturbance in the string of a musical instrument such as a guitar..
Harmonic waves are characterized by being cyclical or periodic. This means that the disturbance repeats itself every certain constant time interval, called period wave.
Harmonic waves can be mathematically modeled using the sine and cosine functions.
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..
Nature presents us with examples of wave motion all the time, sometimes this is obvious, but other times 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. 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 is studied or the way it interacts with matter..
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 exclusive to waves, such as diffraction, for example.
Let's now look at some everyday examples of obvious wave motion:
A soft spring, spring or slinky It consists of a helical spring with which the longitudinal and transverse waves can be visualized, depending on the way in which it is disturbed by one of its ends.
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. 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. It can be shown that the square of the velocity of the wave vtwo is given by:
vtwo = T / μ
Where T is the tension in the string and μ is its linear density, that is, its mass per unit length.
We have the vocal cords, with which sounds are emitted for communication. Its vibration is perceived by placing the fingers on the throat when speaking.
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..
The Earth is not a static body, since disturbances occur inside it that travel through the different layers. They are perceived as tremors and occasionally, when they carry a lot of energy, as earthquakes capable of causing a lot of damage.
Modern atomic theories explain the structure of the atom by analogy with standing waves.
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
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
Previously, the relationship between speed, wavelength and period had been established as:
v = λ / T
Therefore the period is:
T = λ / v = 2 cm / 4 cm / s = 0.5 s.
Since the frequency is the inverse of the period:
f = 1 / T = 1 / 0.5 s = 2 s-1
The inverse of a second or s-1 It 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.
A string is stretched under the action of a 125 N force. If its linear density μ is 0.0250 kg / m, what will be the velocity of propagation of a wave??
Previously we had seen that the speed depends on the tension and the linear density of the rope as:
vtwo = T / μ
Therefore:
vtwo = 125 N / 0.0250 kg / m = 5000 (m / s)two
Taking the square root of this result:
v = 70.7 m / s
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