To find the wavelength you need. Wavelength and propagation speed

During the lesson you will be able to independently study the topic “Wavelength. Wave propagation speed." In this lesson you will learn about the special characteristics of waves. First of all, you will learn what wavelength is. We will look at its definition, how it is designated and measured. Then we will also take a closer look at the speed of wave propagation.

To begin with, let us remember that mechanical wave is a vibration that propagates over time in an elastic medium. Since it is an oscillation, the wave will have all the characteristics that correspond to an oscillation: amplitude, oscillation period and frequency.

In addition, the wave has its own special characteristics. One of these characteristics is wavelength. The wavelength is denoted by the Greek letter (lambda, or they say “lambda”) and is measured in meters. Let us list the characteristics of the wave:

What is wavelength?

Wavelength - this is the smallest distance between particles vibrating with the same phase.

Rice. 1. Wavelength, wave amplitude

It is more difficult to talk about wavelength in a longitudinal wave, because there it is much more difficult to observe particles that perform the same vibrations. But there is also a characteristic - wavelength, which determines the distance between two particles performing the same vibration, vibration with the same phase.

Also, the wavelength can be called the distance traveled by the wave during one period of oscillation of the particle (Fig. 2).

Rice. 2. Wavelength

The next characteristic is the speed of wave propagation (or simply wave speed). Wave speed denoted in the same way as any other speed, by a letter and measured in . How to clearly explain what wave speed is? The easiest way to do this is using a transverse wave as an example.

Transverse wave is a wave in which disturbances are oriented perpendicular to the direction of its propagation (Fig. 3).

Rice. 3. Transverse wave

Imagine a seagull flying over the crest of a wave. Its flight speed over the crest will be the speed of the wave itself (Fig. 4).

Rice. 4. To determine the wave speed

Wave speed depends on what the density of the medium is, what the forces of interaction between the particles of this medium are. Let's write down the relationship between wave speed, wave length and wave period: .

Velocity can be defined as the ratio of the wavelength, the distance traveled by the wave in one period, to the period of vibration of the particles of the medium in which the wave propagates. In addition, remember that the period is related to frequency by the following relationship:

Then we get a relationship that connects speed, wavelength and oscillation frequency: .

We know that a wave arises as a result of the action of external forces. It is important to note that when a wave passes from one medium to another, its characteristics change: the speed of the waves, the wavelength. But the oscillation frequency remains the same.

Bibliography

1. Sokolovich Yu.A., Bogdanova G.S. Physics: a reference book with examples of problem solving. - 2nd edition repartition. - X.: Vesta: publishing house "Ranok", 2005. - 464 p.
2. Peryshkin A.V., Gutnik E.M., Physics. 9th grade: textbook for general education. institutions / A.V. Peryshkin, E.M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300 p.

1. Internet portal "eduspb" ()
2. Internet portal "eduspb" ()
3. Internet portal “class-fizika.narod.ru” ()

Homework

A body oscillating in an elastic medium creates a disturbance that is transmitted from one point to another and is called a wave. This happens at a certain speed, which is considered the speed of its spread. That is, this is a quantity that characterizes the distance traveled by any point on the wave in a unit period of time.

Let the wave move along one of the axes (for example, horizontal). Its shape repeats itself in space after a certain time, that is, the wave profile moves along the propagation axis at a constant speed. During the corresponding time, its front will shift by a distance called the wavelength.

It turns out that the wavelength is the very distance that its front “travels” in a period of time equal to the oscillation period. For clarity, let’s imagine a wave in the form in which it is usually depicted in drawings. We all remember what they look like, for example: The wind drives them along the sea, and each wave has a crest and the lowest point (minimum), and both of them are constantly moving and replacing each other. Points lying in the same phase are the tops of two adjacent crests (let us assume that the crests have the same height and the movement occurs at a constant speed) or the two lowest points of adjacent waves. The wavelength is precisely the distance between such points (two adjacent crests).

Everything can travel in the form of waves - heat, light, sound. They all have different lengths. For example, as sound waves pass through the atmosphere, they slightly change the air pressure. The areas of maximum pressure correspond to the maxima of sound waves. Due to its structure, the human ear detects these pressure changes and sends signals to the brain. This is how we hear sound.

The length of a sound wave determines its properties. To find it, you need to divide (measured in m/sec) by the frequency in Hz. Example: At a frequency of 688 Hz, a sound wave moves at a speed of 344 m/sec. The wavelength in this case will be equal to 344: 688 = 0.5 m. It is known that the speed of wave propagation in the same medium does not change, therefore, its length will depend on the frequency. Low frequencies have a longer wavelength than high frequencies.

An example of another type of electromagnetic radiation is a light wave. Light is the part of the electromagnetic spectrum visible to our eyes. The wavelength of light that human vision can perceive ranges from 400 to 700 nm (nanometers). On both sides of the visible range of the spectrum lie areas that are not perceived by our eyes.

Ultraviolet waves have a wavelength shorter than the visible part of the spectrum. Although the human eye is not able to see them, they are nevertheless capable of causing considerable harm to our vision.

The wavelength is longer than the maximum length that we can see. These waves are captured by special equipment and used, for example, in night vision cameras.

Among the rays accessible to our vision, the violet ray has the shortest length, and the red one has the longest. In between them lies the entire visible spectrum (remember the rainbow!)

How do we perceive colors? Light rays of a certain length fall on the retina of the eye, which has light-sensitive receptors. These receptors transmit signals directly to our brain, where the sensation of a certain color is formed. Exactly what colors we see depends on the wavelengths of the incident rays, and the brightness of the color sensation is determined by the intensity of the radiation.

All objects around us have the ability to reflect, transmit or absorb incident light (in whole or in part). For example, the green color of foliage means that from the entire range, mainly green rays are reflected, the rest are absorbed. Transparent objects tend to block radiation of a certain length, which is used, for example, in filter photography).

Thus, the color of an object tells us about its ability to reflect waves of a certain part of the spectrum. We see objects that reflect the entire spectrum as white, and objects that absorb all rays as black.

WHAT ARE RADIO WAVES

Radio waves are electromagnetic waves that travel through space at the speed of light (300,000 km/sec). By the way, light is also electromagnetic waves that have properties similar to radio waves (reflection, refraction, attenuation, etc.).

Radio waves carry energy emitted by an electromagnetic oscillator through space. And they are born when the electric field changes, for example, when an alternating electric current passes through a conductor or when sparks jump through space, i.e. a series of rapidly successive current pulses.

Electromagnetic radiation is characterized by frequency, wavelength and power of transferred energy. The frequency of electromagnetic waves shows how many times per second the direction of the electric current changes in the emitter and, therefore, how many times per second the magnitude of the electric and magnetic fields changes at each point in space. Frequency is measured in hertz (Hz), a unit named after the great German scientist Heinrich Rudolf Hertz. 1 Hz is one vibration per second, 1 megahertz (MHz) is a million vibrations per second. Knowing that the speed of electromagnetic waves is equal to the speed of light, we can determine the distance between points in space where the electric (or magnetic) field is in the same phase. This distance is called the wavelength. The wavelength in meters is calculated using the formula:

Or approximately
where f is the frequency of electromagnetic radiation in MHz.

The formula shows that, for example, a frequency of 1 MHz corresponds to a wavelength of approx. 300 m. As the frequency increases, the wavelength decreases, with a decrease - guess for yourself. Later we will see that the wavelength directly affects the length of the antenna for radio communication.

Electromagnetic waves travel freely through air or outer space (vacuum). But if a metal wire, antenna or any other conducting body meets on the path of the waves, then they give up their energy to it, thereby causing an alternating electric current in this conductor. But not all the wave energy is absorbed by the conductor; part of it is reflected from its surface and either goes back or is scattered in space. By the way, this is the basis for the use of electromagnetic waves in radar.

Another useful property of electromagnetic waves is their ability to bend around certain obstacles in their path. But this is only possible when the dimensions of the object are smaller than the wavelength or comparable to it. For example, in order to detect an aircraft, the length of the locator radio wave must be less than its geometric dimensions (less than 10 m). If the body is longer than the wavelength, it can reflect it. But it may not reflect it. Consider the military's Stealth technology, which uses geometric shapes, radio-absorbing materials, and coatings to reduce the visibility of objects to locators.

The energy carried by electromagnetic waves depends on the power of the generator (emitter) and the distance to it. Scientifically, it sounds like this: the energy flow per unit area is directly proportional to the radiation power and inversely proportional to the square of the distance to the emitter. This means that the communication range depends on the power of the transmitter, but to a much greater extent on the distance to it.

SPECTRUM DISTRIBUTION

Radio waves used in radio engineering occupy the region, or more scientifically, spectrum from 10,000 m (30 kHz) to 0.1 mm (3,000 GHz). This is only part of the vast spectrum of electromagnetic waves. Radio waves (in decreasing length) are followed by thermal or infrared rays. After them comes a narrow section of visible light waves, then a spectrum of ultraviolet, x-rays and gamma rays - all these are electromagnetic vibrations of the same nature, differing only in wavelength and, therefore, frequency.

Although the entire spectrum is divided into regions, the boundaries between them are tentatively outlined. The regions follow one another continuously, transition into one another, and in some cases overlap.

By international agreements, the entire spectrum of radio waves used in radio communications is divided into ranges:

But these ranges are very extensive and, in turn, are divided into sections that include the so-called broadcasting and television ranges, ranges for land and aviation, space and sea communications, for data transmission and medicine, for radar and radio navigation, etc. Each radio service is allocated its own section of the spectrum or fixed frequencies.

Allocation of spectrum between different services.

This breakdown is quite confusing, so many services use their own "internal" terminology. Typically, when designating ranges allocated for land mobile communications, the following names are used:

The official names of frequency ranges should not be confused with the names of sections allocated for various services. It is worth noting that the world's major manufacturers of equipment for mobile land communications produce models designed to operate within these particular areas.

In the future, we will talk about the properties of radio waves in relation to their use in land mobile radio communications.

HOW RADIO WAVES PROPADE

Radio waves are emitted through an antenna into space and propagate as electromagnetic field energy. And although the nature of radio waves is the same, their ability to propagate strongly depends on the wavelength.

The earth is a conductor of electricity for radio waves (albeit not a very good one). Passing over the surface of the earth, radio waves gradually weaken. This is due to the fact that electromagnetic waves excite electric currents in the surface of the earth, which consumes part of the energy. Those. energy is absorbed by the earth, and the more, the shorter the wavelength (higher the frequency).

In addition, the wave energy weakens also because the radiation propagates in all directions of space and, therefore, the further the receiver is from the transmitter, the less energy falls per unit area and the less it gets into the antenna.

Transmissions from long-wave broadcast stations can be received at distances of up to several thousand kilometers, and the signal level decreases smoothly, without jumps. Medium wave stations can be heard within a range of thousands of kilometers. As for short waves, their energy decreases sharply with distance from the transmitter. This explains the fact that at the dawn of the development of radio, waves from 1 to 30 km were mainly used for communication. Waves shorter than 100 meters were generally considered unsuitable for long-distance communications.

However, further studies of short and ultrashort waves showed that they quickly attenuate when they travel near the Earth's surface. When the radiation is directed upward, short waves return back.

Back in 1902, the English mathematician Oliver Heaviside and the American electrical engineer Arthur Edwin Kennelly almost simultaneously predicted that there is an ionized layer of air above the Earth - a natural mirror that reflects electromagnetic waves. This layer was called the ionosphere.

The Earth's ionosphere should have made it possible to increase the range of propagation of radio waves to distances exceeding line of sight. This assumption was experimentally proven in 1923. Radio frequency pulses were transmitted vertically upward and the returning signals were received. Measuring the time between sending and receiving pulses made it possible to determine the height and number of reflection layers.

Propagation of long and short waves.

After being reflected from the ionosphere, short waves return to the Earth, leaving hundreds of kilometers of “dead zone” underneath. Having traveled to the ionosphere and back, the wave does not “calm down”, but is reflected from the surface of the Earth and again rushes to the ionosphere, where it is again reflected, etc. Thus, being reflected many times, a radio wave can circle the globe several times.

It has been established that the reflection height depends primarily on the wavelength. The shorter the wave, the higher the height at which it is reflected and, therefore, the larger the “dead zone”. This dependence is true only for the short-wave part of the spectrum (up to approximately 25–30 MHz). For shorter wavelengths the ionosphere is transparent. The waves penetrate through it and go into outer space.

The figure shows that reflection depends not only on frequency, but also on the time of day. This is due to the fact that the ionosphere is ionized by solar radiation and gradually loses its reflectivity with the onset of darkness. The degree of ionization also depends on solar activity, which varies throughout the year and from year to year on a seven-year cycle.

Reflective layers of the ionosphere and the propagation of short waves depending on frequency and time of day.

VHF radio waves have properties more similar to light rays. They are practically not reflected from the ionosphere, bend around the earth's surface very slightly and spread within the line of sight. Therefore, the range of ultrashort waves is short. But this has a definite advantage for radio communications. Since waves in the VHF range propagate within line of sight, radio stations can be located at a distance of 150–200 km from each other without mutual influence. This allows neighboring stations to reuse the same frequency.

Propagation of short and ultrashort waves.

The properties of radio waves in the DCV and 800 MHz ranges are even closer to light rays and therefore have another interesting and important property. Let's remember how a flashlight works. Light from a light bulb located at the reflector's focal point is collected into a narrow beam of rays that can be sent in any direction. Much the same can be done with high-frequency radio waves. They can be collected by antenna mirrors and sent out in narrow beams. It is impossible to build such an antenna for low-frequency waves, since its dimensions would be too large (the diameter of the mirror must be much larger than the wavelength).

The possibility of directed radiation of waves makes it possible to increase the efficiency of the communication system. This is due to the fact that a narrow beam provides less energy dissipation in side directions, which allows the use of less powerful transmitters to achieve a given communication range. Directional radiation creates less interference with other communication systems that are not in the beam range.

Radio wave reception can also take advantage of directional radiation. For example, many are familiar with parabolic satellite antennas, which focus the radiation of the satellite transmitter to the point where the receiving sensor is installed. The use of directional receiving antennas in radio astronomy has made it possible to make many fundamental scientific discoveries. The ability to focus high-frequency radio waves has ensured their widespread use in radar, radio relay communications, satellite broadcasting, wireless data transmission, etc.

Parabolic directional satellite dish (photo from ru.wikipedia.org).

It should be noted that as the wavelength decreases, the attenuation and absorption of energy in the atmosphere increases. In particular, the propagation of waves shorter than 1 cm begins to be affected by such phenomena as fog, rain, clouds, which can become a serious obstacle that limits the communication range.

We have learned that radio waves have different propagation properties depending on the wavelength, and each part of the radio spectrum is used where its advantages are best exploited.

An important physical parameter necessary for solving many problems in acoustics and radio electronics. It can be calculated in several ways, depending on what parameters are specified. It is most convenient to do this if you know the frequency or period and speed of propagation.

Formulas

The basic formula that answers the question of how to find wavelength through frequency is presented below:

Here l is the wavelength in meters, v is the speed of its propagation in m/s, u is the linear frequency in hertz.

Since frequency is related to period in an inverse relationship, the previous expression can be written differently:

T is the oscillation period in seconds.

This parameter can be expressed in terms of cyclic frequency and phase speed:

l = 2 pi*v/w

In this expression, w is the cyclic frequency expressed in radians per second.

The frequency of the wave through the length, as can be seen from the previous expression, is found as follows:

Let's consider an electromagnetic wave that propagates in a substance with n. Then the frequency of the wave in terms of length is expressed by the following relation:

If it propagates in a vacuum, then n = 1, and the expression takes on the following form:

In the last formula, the wave frequency in terms of length is expressed using the constant c - the speed of light in vacuum, c = 300,000 km/s.

Wavelength

Examples

Approximately, with an error of about 0.07%, you can calculate the radio wavelength as follows: 300 divided by the frequency in megahertz, we get the wavelength in meters, for example for 80 Hz, the wavelength is 3750 kilometers, for 89 MHz - 3.37 meters, for 2 .4 GHz - 12.5 cm.

The exact formula for calculating the wavelength of electromagnetic radiation in a vacuum is:

where is the speed of light, equal in the International System of Units (SI) to 299,792,458 m/s exactly.

To determine the wavelength of electromagnetic radiation in any medium, use the formula:

where is the refractive index of the medium for radiation with a given frequency.

Notes

Literature

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See what “Wavelength” is in other dictionaries:

The distance between the two closest points of a harmonic wave that are in the same phase. Wavelength λ = vT, where T is the oscillation period, ? phase speed of the wave. * * * WAVELENGTH WAVELENGTH, the distance between the two nearest points... ... encyclopedic Dictionary

wavelength- (λ) The distance by which the surface of an equal phase wave moves during one period of oscillation. [GOST 7601 78] wavelength The distance traveled by an elastic wave in a time equal to one full period of oscillation. )