Electromagnetic wave

Representation the wavelength of a function sine
The wavelength is a physical, homogeneous size with a length, used to characterize periodic phenomena. Alfred Perot and Charles Fabry determine the value of the international meter in wavelength using a semi-silvered blade interferometer.


A wave is a physical phenomenon being propagated and which reproduces identical to itself a little later in time and a little further in space. One can then define the wavelength as being the short-haul separating two points of the wave strictly identical to a given moment.
One commonly indicates it by the Greek letter lambda).
The wavelength is the space equivalent of the temporal period. Indeed, the wavelength is the distance covered by the wave during one period. If one calls C the celerity of the wave and T his period temporal, one a:
λ = cT = c ⁄ v
In the vacuum, the wavelength is noted λ0. One has then, in a medium of index N, the relation:
λ0 = nλ

Approaches mathematical

Axis X represents the distances covered, and is there the value at a given moment of a quantity which varies (for example pressure of the air for a sound wave or intensity of the electric field or magnetic of one light wave).
ƒ (x + λ) = ƒ (x)
By analogy with the homonymous mathematical concept, one names it also sometimes improperly period. In physics, the period is the temporal equivalent wavelength: the period is the minimal time which passes between two identical repetitions of the wave in the same point. For a sinusoidal wave, the wavelength is the distance between two of the same peaks signs successive.
The wavelength is proportional to the period, and thus inversely proportional to the frequency, the number of of the same nodes signs which cross a point in one duration of one second. The wavelength is equal at the speed of the wave divided by the frequency of passage.

Vector of wave and number of wave

With each wavelength is associated a number of wave and a vector with wave.
The number of wave is a size proportional to the number of oscillations which a wave by a unit of length carries out : it is the number wavelengths present on a distance from 2 magpie units of length. This number of wave is thus a size inversely proportional to the wavelength. Its unit is the radian per meter.
The vector of wave (or vector of phase, in electronics in particular) is a vector representing a wave. The standard of the vector corresponds to the number of wave (dependant contrary the wavelength), and its direction indicates the direction of propagation wave.
The vector of wave is very useful to generalize the equation of one wave to the description of a family of waves. If all the waves of a family are propagated in the same direction and have the same wavelength, they all can be described by the same vector of wave. The case more the current of a family of wave observing these conditions is that of a plane wave, for which the family of waves is also coherent (all the waves have the same phase).

Electromagnetic wave

When one is in the case of an electromagnetic wave being propagated in the vacuum, this speed is speed of light C in the vacuum, and the relation is written:
λ0 = c ⁄ v
λ is the wavelength in the vacuum of the wave
C is speed of light (≈3×108 m ⁄ s)
ν is the frequency of the wave.
The electromagnetic wave is a model used to represent the electromagnetic radiations. It is associated with the concept of photon.
It is advisable to distinguish well:
the electromagnetic radiation, which is the studied phenomenon, and
the electromagnetic wave, which is one of the representations of the phenomenon.
One light wave is an electromagnetic wave of which the wavelength corresponds to the visible spectrum, that is to say between the 780 Nm and wavelengths 380, which corresponds to energies of photon from 1.5 to 3 eV.


Like all the waves, an electromagnetic wave can be analyzed by using the spectral analysis, one can break up the wave into waves known as monochromatic.
electromagnetic wave: coupled oscillation of the electric field and the magnetic field, model of the vibrating dipole (the trihedron must be direct)
(k, E, B
A monochromatic electromagnetic wave can be modelled by a vibrating electrostatic dipole, this suitably reflecting model, for example, the oscillations of the electronic cloud of an atom intervening in the diffusion Rayleigh (model of the electron elastically dependant).
The variations of the fields electric and magnetic are bound by the Maxwells equations, one can thus represent the wave by only one of these fields, in general the electric field. One can then write the general equation of a monochromatic plane wave:
E (r, t) = cos (ωt - k * r + φ) * E0
ω is the pulsation and is worth 2 π c ⁄ λ
r is the vector position of the point considered
k is the vector of wave whose standard is worth 2 π ⁄ λ being the wavelength
φ is the phase in the beginning.
The complex form is also frequently used:
E (r, t) = ei * (ωt - k * r + φ) * E0
One will then obtain the sizes physical, real, by taking the real part of this complex form.



Polarization corresponds to the direction and the amplitude of the electric field E . For a wave nonpolarized, or natural, E turns around its axis in a random and unforeseeable way during time. To polarize a wave corresponds to give a trajectory defined in the electric field. There are several kinds of polarization:
Linear polarization when E always remains in the same plan.
Circular polarization, the electric field turns around its axis by forming a circle.
Elliptic polarization, the electric field turns around its axis and changes amplitude to form an ellipse.

Undulatory behavior

In a homogeneous and isotropic medium, the electromagnetic wave is propagated in straight line. At the time of the meeting with an obstacle, there is diffraction, during a change of medium, there is reflection and refraction, there is also refraction if the properties of the medium change according to the place (heterogeneity).
During a change of propagation medium, part of the electromagnetic wave sets out again about the middle of origin, it is the reflection.
The most known case of the reflection is the mirror, but this one also relates to the X-rays (mirror with X-rays) and the waves radio: reflection on the ionosphere of the waves megahertz, parabolic aerial, reflection on the Moon
During a change of propagation medium, if the second medium is transparent for the wave, this one is propagated in the second medium but with a different direction. That relates to the light (lens optical, mirage), but also the radio waves (refraction of the decametric waves in the ionosphere).
When a wave meets an atom, it is diffused on this one, it changes direction. One distinguishes the diffusion Rayleigh, known as electronic diffusion, during which the wave does not change a wavelength, the Raman diffusion which are an electronic diffusion with reduction or increase wavelength, and the Compton diffusion, in the case of X-rays diffusing on light atoms, during which the wavelength increases.
Like all the waves, the electromagnetic waves can interfere. In the case of the radiocommunications, that causes an interference of the signal
The interference of diffused waves bears the name of diffraction:
theory of diffraction
diffraction by a slit
slits of Young
diffraction pattern
diffraction of X-rays
reciprocal space.
Flow of energy
The flow of energy through a surface is given by the flow of the vector of Poynting.

Duality wave-corpuscle

The concept of wave electromagnetic is complementary to that of photon. In fact, the wave provides a more relevant description of radiation for the weak frequencies (that is to say big wavelengths) like the radio waves.
In fact, the electromagnetic wave represents two things:
macroscopic variation of the electric field and the magnetic field
the function of wave of the photon, that is to say the standard with the square of the wave is the probability of presence of a photon.
When the flow of energy is large in front of the energy of the photons, one can consider that one has a quasi-continuous flow of photons, and the two concepts are recovered. This is not true any more when the flow of energy is weak (one sends the photons one by one), the concept of variation macroscopic (average) then does not have any more a direction.
The flow of energy is given by the vector of Poynting. Each photon carries a determined amount of power, being worth E = H·ν, H being the Plancks constant and ν the frequency. One can thus calculate the flow of photons through a surface.


The undulatory theory of the light was mainly developed by Christiaan Huygens in the years 1670, and by Augustin Fresnel. She was opposed at the time to the corpuscular theory, defended mainly by Rene Descartes. Huygens worked mainly on the laws of reflection and of refraction, Fresnel developed in particular the concepts of interference and wavelength. The undulatory and corpuscular approaches were joined together by Albert Einstein when this one establishes the model of the photon in 1905, in his work on the photoelectric effect.
The large theoretical projection was the synthesis of the laws of electromagnetism by James Clerk Maxwell. The Maxwells equations predicted the speed of the electromagnetic waves, and speed of light measures it showed that the light was of nature electromagnetic.
The radio, low frequency waves and big wavelength, were discovered at the end of the XIX esiècle with work in particular of Alexandre Popov, Heinrich Hertz, Edouard Branly and of Nikola Tesla. The X-rays, high frequency and low wavelength, were discovered by Wilhelm Röntgen in 1895.
A radio wave (known as radio wave) is an electromagnetic wave whose frequency is lower than 3000GHz, that is to say a wavelength higher than 0,1 Misters.

Definition and regulation

The field of the radiocommunications is regulated by the International union of telecommunications (UIT) which established a payment of the radiocommunications in which one can read the following definition :
Radio waves or Hertzian waves: wave electromagnetic whose frequency is by convention lower than 3000GHz, being propagated in space without artificial guide, they lie between 9 Khz and 3000 GHZ which corresponds to wavelengths of 33 km to 0,1 mm
The waves of frequency lower than 9 Khz are however radio waves, but are not regulated.
The waves of frequency higher than 3000 GHZ are classified in the waves infra-red (irda), because technology associated with their use is currently of type optical and nonelectric, but this border is artificial, there is no difference in nature between the radio waves and the light waves (and other electromagnetic waves).

Spectrum radio frequency

Official terminology
A radio wave is classified according to its frequency expressed in Hz or cycles a second, the whole of these frequencies constitutes the spectrum radio frequency. The spectrum is divided conventionally into one decade old tapes, whose international names are standardized. Equivalent French-speaking names are sometimes also used in the French texts.

Other names

To avoid ambiguities with the vocabulary of acoustics and wiring for sound, one uses the term "audiofrequency" preferably with "low frequency" to indicate acoustic waves or electrical signals in the tape 30Hz with 30kHz
Other names of tapes or sub-bands are also used according to the technical practices:
The tapes of the microwaves or "ultra high frequencies" between 400MHz and 30GHz are historically cut out in half-octaves corresponding to the guide of wave standards, called: tapes U, L, S, C, X, K (itself cut out in Ku and Ka). This terminology still is very much used.
The tape of 1600kHz with 3000kHz is often called MHF.
The term "intermediate frequency" indicated the fixed frequency of amplification of the receivers superheterodynes: one prefers today the term to him "frequency intermediate" nonambiguous.
The tapes of broadcasting and terrestrial television also have standardized names: tapes I, II, III in VHF, IV and V in UHF and tapes GO in LF, PO in MF, HF OC.
Lastly, certain tapes received the name of their lawful use: thus, tapes ISM are the tapes allocated with the domestic uses without license


Like all the electromagnetic waves, the radio waves are propagated in empty space with speed of light and with an attenuation proportional to the square of the distance covered according to the equation of telecommunications.
In the atmosphere, they undergo moreover attenuations related to precipitations, and can be considered or guided by the part of the upper atmosphere called ionosphere.
They are attenuated or deviated by the obstacles, according to their wavelength, the nature of material, its form and its dimension. To simplify, a conducting material will have an effect of reflection, whereas a dielectric material produces a deviation, and the effect is related to the relationship between the dimension of the object and the wavelength.


Diagram of attenuation of the atmosphere according to the wavelength. The radio waves of short and average wavelength are not attenuated (restricted parking zone on the right diagram), while the radio waves long wavelength are absorbed (zone chestnut at the right end of the diagram).
Each radioelectric frequency differently undergoes the various effects of propagation, which explains their choice according to the application. Thus, for example, the terrestrial atmosphere blocks the emissions towards space out of certain tapes, which are thus privileged for radioastronomy and the satellites. Certain frequencies are absorbed by the water molecules, therefore used for the microwawe ovens, others on the contrary are reflected by precipitations and are used for radars weather, etc
The other key criterion is the band-width usable and the obstruction of the spectrum by the multiple applications and services: any application requires a band-width, which must be to him affected under penalty of mutual jamming. For example television can use only high frequencies VHF or UHF.
Finally technology available gradually makes it possible to use wavebands increasingly high. Thus, for example the SHF and EHF were not usable before the invention of the magnetron.

Types of modulation of a radio wave

The radio waves are modulated to carry information (a signal), for example in amplitude modulation for radio operator AM, in frequency modulation for the FM radio one, phase modulation in other applications or in modulation of impulse for the radars.

Management and attribution of the radioelectric frequencies

The demand for band-width for telecommunications or the radars, as well as the protection of frequencies of radioastronomy makes radioelectric spectrum a rare resource which must be regulated universally.
The attribution of the radio frequencies is carried out in the framework of international agencies, in particular the World conference of the radiocommunications (CMR) and the International union of telecommunications (UIT).

Health hazards related to the radio waves

The dangers incurred in the presence of intense radioelectric fields were very early raised in particular with the appearance of the microwawe ovens in the hearths, for the people living near the military transmitters of very strong power or for the personnel working close to the radars. More recently, the danger possibly related to the cellphones brought to define a standardized measurement of radiation (Flow of specific absorption or DAS), but the medical effects do not achieve the unanimity of the scientists.

Measure radioelectric spectrum

Professional measurements on the electromagnetic waves require a calibrated antenna adapted to the frequencies to measure, followed by an electronic measuring device of type:
analyzer of spectrum for the measurement of the amplitudes and frequencies of various components of a tape
electromagnetic analyzer of field (or field intensity measuring device) for measurements of electromagnetic compatibility or electric field intensity.
The analysis as an amateur of current tapes LF with UHF can be carried out with a calibrated receiver (scanner). The analysis in tapes low VLF at ELF is carried out in general with softwares FFT after direct digitalization in a personal computer.

Use of the Hertzian wave term

Being the radio waves, the Hertzian waves term" is a synomyme. According to the definition of the UIT, hertzian term the "does not cover that the signals transmitted by radiation - it is the electromagnetic radiation - that is to say without hardware support, for example as well terrestrial television as by wireless-aware satellite and all the other modes of transmission in the frequency spectrum of these waves
NB: The intervals of frequency and wavelengths vary according to the standards and can overlap.

Wavelength of Broglie

Louis de Broglie discovered that all the physical particles equipped with a momentum have a wavelength, named wavelength of Broglie. For a relativistic particle, the wavelength of Broglie is given by
λ = h ⁄ p = h ⁄ mv = h ⁄ ϒm0v = h ⁄ m0v √1 - v² ⁄ c²
where h is the Plancks constant, ϒ the factor of Lorentz, m0 the mass of the particle at rest, v speed, and cspeed of light in the vacuum.

Thermal wavelength of Broglie

The thermal wavelength of Broglie corresponds to the wavelength of typical Broglie of the particles of a gas brought up to a temperature T given. This size intervenes (inter alia) in the discussions justifying that the quantum effects are negligible when one considers a macroscopic volume of gas.

Displacement of an electromagnetic wave

The waves on the surface of the pond is propagated like concentric circles. The radio wave emitted by the isotropic antenna (that is to say radiating in a uniform way in all the directions of space) can be represented by a succession of concentric spheres. One can imagine a bubble very quickly inflating actually with speed of light C, very near to 300000 km a second. One speaks here about wave propagation in free space; in space, for example.
The qualifier of electromagnetic expresses that a radio wave is made of two components: an electric field E and a magnetic field H.Les two fields are perpendicular one to the other, their amplitudes are in constant report ⁄ ratio and their variations are in phase. The measurement of the amplitude of the electric field can be measured using a champmeter. One more often expresses it in µV ⁄ m or in dBµV ⁄ m decibels compared to the microvolt per meter, it is it which is used for to determine the level of reception of a transmitter in a given place.

Relation between electric field and magnetic field, intrinsic impedance of the vacuum

Several wavelengths of the antenna the relationship between the amplitude of the magnetic fields and electric is constant and equal to the intrinsic impedance of the propagation medium:
Z0 = E ⁄ H = √µ ⁄ ε
with :
Z0 : intrinsic impedance of the propagation medium in ohms
E : amplitude of the electric field in V ⁄ m
H : amplitude of the magnetic field in At ⁄ m
µ : permeability of the medium

E: permittivity of the medium

If the propagation medium is the vacuum or the air one a:
Z0 = √µ0 ⁄ ε0 = √(4 * π * 10-7) ⁄ (8,85 * 10-12) = 376,819 = 120 * π
The intrinsic impedance of the vacuum, important parameter of the wave propagation, is of 377 ohms. The presence of p in the result is less astonishing if one replaces the permittivity of the vacuum by 1 (36 .109) his approximate value.

Propagation velocity

The propagation velocity of an electromagnetic wave in a medium of permeability µ and permittivity E is given by the formula:
v = √1 ⁄ µ * ε
By replacing µ and E by the permeability and the permittivity of the vacuum one can calculate C, the propagation velocity of the waves which is also the céléritéde the light:
c = √1 ⁄ 8,854 * 10-12 * 4 * π * 10-7 ≈ 300000000 m ⁄ s

Surface density of power

At the distance D of the isotropic radiator radiating a power P, one can calculate the power distributed on a m ² of the surface of the sphere of radius D, in other words the surface density of power in W ⁄ m ², by dividing P by the surface of the sphere = 4pd ², the vector of Poynting is the product of the vectors E and H of the wave. At the distance D, its module S is equal to the surface density of power.
One can thus write:
S = E² ⁄ µ0 * c = P ⁄ 4 * π * d²
After replacement of C by his value according to µ and E then to have simplified and finally to have introduced the intrinsic impedance of the vacuum one obtains the relation between E, P and D

Polarization of the wave

It corresponds to the orientation of its electric field : if that-is vertical, polarization is vertical. A dipole whose conductor is horizontal radiates a horizontally polarized wave. Certain antennas have a circular polarization, particular case of elliptic polarization. When the field E always varies in the same plan polarization is linear.

Example wavelength

French-speaking designation Frequency Wavelength Other names Examples of use
EBF (super low frequency) 3 Hz with 30 Hz 100000km with 10000km   Detection of natural phenomena
SBF (super low frequency) 30Hz with 300Hz 10000km with 1000km   Communication with the submarines
UBF (ultra low frequency) 300Hz with 3000Hz 1000km with 100km   Detection of natural phenomena
TBF (very low frequency) 3kHz with 30kHz 100km with 10km myriametric waves Communication with the submarines, Implants medical, Scientific research
BF (low frequency) 30kHz with 300kHz 10km with 1km long waves or long or kilometric waves Radionavigation, Broadcasting GO, Radio-identification
MF (intermediate frequency) 300kHz with 3MHz 1km with 100m small waves or medium waves or hectometric Radio operator AM, Apparatus of search for victims of avalanche
HF (high frequency) 3MHz with 30MHz 100m with 10m short waves or decametric Communication for the flights length mail, Radio-identification
THF (very high frequency) 30MHz with 300MHz 10m with 1m ultra-short or metric waves FM radio, Television
UHF (ultra high frequency) 300MHz with 3GHz 1m with 10cm decimetre waves GSM, GPS, Wi-Fi, Television
SHF (super high frequency) 3GHz with 30GHz 10cm with 1cm centimetric waves Microwave
EHF (extremely high frequency) 30GHz with 300GHz 1cm with 1mm millimetre-length waves Anti-collision radars for cars, transportable video Connections
Terahertz 300GHz with 3000GHz 1mm with 100µm submillimeter waves  

Measure electromagnetic fields

The wavelength and the frequency characterize the electric fields and magnetic. The wavelength is the distance covered by a wave in a cycle of oscillation and is measured in meters the frequency is measured by the number of cycles a second and the unit is the Hertz (Hz). A cycle a second equal a Hertz. One kilocycle (Khz) equalizes 1000 Hertz, one megahertz equalizes a million Hertz and a gigahertz equalizes a billion Hertz. The frequency of a wave is inversely proportional to its length. The mathematical formula is simple: The frequency multiplied by the wavelength is equal to speed of light. To 50 Hz, the wavelength is of 6.000 km while to 100 MHz, the wavelength is of 3 meters.
The electromagnetic spectrum is divided into ionizing and nonionizing bands, according to the impact of the waves on biological fabrics. Ionization occurs when an electron is withdrawn from its normal position in the atom or the molecule and can damage fabrics, even the genetic luggage. The ionizing portion of the electromagnetic spectrum includes ⁄ understands the ultraviolet rays and the gamma rays and X. the wavelength is then very short and the very high frequency and the intensity. The not-ionizing portion includes ⁄ understands the waves megametric, the radio waves, the microwaves in the bands frequency of radio communication, the infra-reds and the visible light. The radio waves generally lie between 30 Khz and 300 GHZ. The microwaves are a category of radio waves.
The electromagnetic spectrum
B = µH, µ represents the magnetic permeability. For the low frequencies, like the electric lines, one uses usually the units of density of the magnetic flux. The magnetic field is thus expressed out of Mg (milliGauss) or lT (microTesla) where 1 Mg = 10 lT. The ground produces a static magnetic field which extends from 350 to 700 milliGauss (Mg), on the surface of the planet and which varies slightly according to the daily and annual rates ⁄ pace. There exists also a natural electric field resulting from the variation of the difference in loads between the ground and the atmosphere.
For the radio frequency, the measuring unit used depends on if the energy source is distant or close the exposed person. The density of being able is used in field moved away, C. - with-D. when measurement is taken at a distance of several wavelengths of source RF. Television, the radio, the antennas and the turns of transmission of cell phone are sources in distant field. Density of being able definite as the rate of energy which circulates through a known surface. It is measured in Watts per square meter (W ⁄ m2, but in mW ⁄ m ² gold ⁄ cm ²). (One MW equal 0,001 Watt of power and a µW equalizes 0,000001 Watt).
Therefore, 1mW ⁄ cm² = 1,000 µW ⁄ cm² or 10 W ⁄ m², on another side, the exposure in close field is the exposure near an electromagnetic source. The cell phones, rifles radar and certain electric household appliances are examples of radiation source in close field. For the exposure in close field, one uses the specific flow of absorption (DAS). One defines it as the rate of energy absorption per unit of mass and expresses one self in W ⁄ kg. The DAS measures amount of power RF absorptive by the body.

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