List three “rules of thumb” that apply to the different frequencies follow me the electromagnetic spectrum.Explain why the greater the frequency, the much shorter the wavelength of an electromagnetic wave.Draw a simplified electromagnetic spectrum, describe the family member positions, frequencies, and also spacing that the different species of radiation bands.List and explain the various methods whereby electromagnetic waves room produced across the spectrum.

You are watching: An electromagnetic wave has a frequency of 12 mhz. what is its wavelength in vacuum?

In this module us examine how electromagnetic waves space classified into categories such together radio, infrared, ultraviolet, and so on, so that we can understand several of their similarities and also some of your differences. Us will additionally find the there are numerous connections v previously debated topics, such as wavelength and also resonance. A short overview of the production and also utilization that electromagnetic waves is discovered in Table 1.

Table 1. Electromagnetic WavesType that EM waveProductionApplicationsLife sciences aspectIssues
Radio & TVAccelerating chargesCommunications far controlsMRIRequires controls for tape use
MicrowavesAccelerating fees & heat agitationCommunications, ovens, radarDeep heatingCell phone call use
InfraredThermal agitations & electronic transitionsThermal imaging, heatingAbsorbed by atmosphereGreenhouse effect
Visible lightThermal agitations & electronic transitionsAll pervasivePhotosynthesis, human vision
UltravioletThermal agitations & digital transitionsSterilization, Cancer controlVitamin D productionOzone depletion, Cancer causing
X-raysInner electronic transitions and fast collisionsMedical SecurityMedical diagnosis, Cancer therapyCancer causing
Gamma raysNuclear decayNuclear medicine, SecurityMedical diagnosis, Cancer therapyCancer causing, Radiation damage

Connections: Waves

There room many types of waves, such as water waves and even earthquakes. Among the many shared qualities of waves room propagation speed, frequency, and also wavelength. This are constantly related by the expression vW=. This module concentrates on EM waves, yet other modules contain instances of every one of these attributes for sound waves and submicroscopic particles.

As listed before, one electromagnetic wave has actually a frequency and also a wavelength connected with it and travels in ~ the rate of light, or c. The relationship amongst these wave features can be explained by vW = , where vW is the propagation rate of the wave, f is the frequency, and λ is the wavelength. Here vW = c, so that for every electromagnetic waves, .

Thus, for every electromagnetic waves, the greater the frequency, the smaller sized the wavelength.

Figure 1 shows how the various species of electromagnetic waves room categorized follow to their wavelengths and also frequencies—that is, it shows the electromagnetic spectrum. Many of the qualities of the various types of electromagnetic tide are concerned their frequencies and also wavelengths, together we candlestick see.


Figure 3. Very long wavelength radio waves are necessary to reach this submarine, requiring exceptionally low frequency signals (ELF). Shorter wavelengths do not pass through to any significant depth.

AM radio waves are supplied to bring commercial radio signal in the frequency range from 540 to 1600 kHz. The abbreviation AM represents amplitude modulation, i m sorry is the technique for placing details on these waves. (See Figure 4.) A carrier wave having actually the an easy frequency the the radio station, speak 1530 kHz, is differed or modulated in amplitude by one audio signal. The resulting wave has a constant frequency, but a differing amplitude.

A radio recipient tuned to have actually the exact same resonant frequency as the carrier wave have the right to pick up the signal, if rejecting the numerous other frequencies impinging ~ above its antenna. The receiver’s circuitry is designed come respond come variations in amplitude of the carrier wave to replicate the initial audio signal. The audio signal is intensified to journey a speaker or perhaps to it is in recorded.


Figure 5. Frequency modulation because that FM radio. (a) A carrier tide at the station’s simple frequency. (b) an audio signal in ~ much lower audible frequencies. (c) The frequency the the carrier is modulated by the audio signal without transforming its amplitude.

FM radio waves are also used for commercial radio transmission, however in the frequency variety of 88 to 108 MHz. FM stands for frequency modulation, another method of transporting information. (See Figure 5.) right here a carrier wave having actually the basic frequency that the radio station, perhaps 105.1 MHz, is modulated in frequency through the audio signal, developing a tide of constant amplitude but varying frequency.

Since audible frequencies variety up to 20 kHz (or 0.020 MHz) at most, the frequency of the FM radio wave have the right to vary native the transport by as lot as 0.020 MHz. For this reason the transport frequencies that two various radio stations cannot be closer than 0.020 MHz. An FM recipient is tuned come resonate in ~ the carrier frequency and also has circuitry the responds come variations in frequency, reproducing the audio information.

FM radio is naturally less topic to noise indigenous stray radio sources than am radio. The factor is the amplitudes of waves add. For this reason an to be receiver would analyze noise included onto the amplitude the its carrier tide as component of the information. One FM receiver can be make to reject amplitudes various other than the of the basic carrier wave and also only look because that variations in frequency. It is thus simpler to disapprove noise from FM, since noise produces a sports in amplitude.

Television is likewise broadcast on electromagnetic waves. Due to the fact that the waves must lug a good deal that visual and also audio information, each channel needs a larger selection of frequencies than an easy radio transmission. TV channels utilize frequencies in the range of 54 to 88 MHz and also 174 come 222 MHz. (The whole FM radio tape lies between channels 88 MHz and also 174 MHz.) this TV networks are called VHF (for very high frequency). Other networks called UHF (for ultra high frequency) make use of an even higher frequency variety of 470 come 1000 MHz.

The TV video signal is AM, if the TV audio is FM. Keep in mind that these frequencies space those of free transmission through the user utilizing an old-fashioned roof antenna. Satellite dishes and cable transmission of TV occurs at significantly greater frequencies and is swiftly evolving through the use of the high-definition or HD format.

Example 1. Calculating wavelength of Radio Waves

Calculate the wavelength of a 1530-kHz to be radio signal, a 105.1-MHz FM radio signal, and a 1.90-GHz mobile signal.


The relationship in between wavelength and also frequency is , where c = 3.00 × 108 m/s is the speed of light (the rate of light is only an extremely slightly smaller sized in air 보다 it is in a vacuum). We have the right to rearrange this equation to discover the wavelength because that all three frequencies.


Rearranging gives \\lambda=\\fraccf\\\\.

For the f = 1530 kHz AM radio signal:

\\beginarraylll\\lambda&=&\\frac3.00\\times10^8\\text m/s1530\\times10^3\\text cycles/s\\\\\\text &=&196\\text m\\endarray\\\\

For the = 105.1 MHz FM radio signal:

\\beginarraylll\\lambda&=&\\frac3.00\\times10^8\\text m/s105.1\\times10^6\\text cycles/s\\\\\\text &=&2.85\\text m\\endarray\\\\

And because that the = 1.90 GHz cell phone:

\\beginarraylll\\lambda&=&\\frac3.00\\times10^8\\text m/s1.90\\times10^9\\text cycles/s\\\\\\text &=&0.158\\text m\\endarray\\\\


These wavelengths are continuous with the spectrum in Figure 1. The wavelengths are additionally related to various other properties of this electromagnetic waves, together we candlestick see.

The wavelengths discovered in the preceding instance are representative the AM, FM, and also cell phones, and account for several of the distinctions in just how they room broadcast and how fine they travel. The most reliable length for a linear antenna, such as questioned in manufacturing of Electromagnetic Waves, is \\frac\\lambda2\\\\, half the wavelength that the electromagnetic wave. Hence a very big antenna is required to properly broadcast typical AM radio with its transport wavelengths ~ above the stimulate of numerous meters.

One benefit to these lengthy AM wavelength is that they have the right to go over and also around rather huge obstacles (like buildings and also hills), just as ocean waves can go around big rocks. FM and TV are finest received once there is a line of sight in between the transfer antenna and receiver, and also they are often sent from very tall structures. FM, TV, and mobile call antennas themselves are lot smaller than those offered for AM, however they room elevated to attain an unobstructed line of sight. (See Figure 6.)


Figure 7. An image of Sif Mons with lava flows on Venus, based on Magellan artificial aperture radar data merged with radar altimetry to produce a three-dimensional map that the surface. The Venusian setting is opaque to clearly shows light, however not come the microwaves that were supplied to create this image. (credit: NSSDC, NASA/JPL)

Since that is feasible to carry much more information per unit time on high frequencies, microwaves are quite suitable for communications. Many satellite-transmitted info is brought on microwaves, as room land-based long-distance transmissions. A clear line of sight in between transmitter and also receiver is needed due to the fact that of the quick wavelengths involved.

Radar is a common application that microwaves the was first developed in world War II. By detecting and timing microwave echoes, radar systems have the right to determine the distance to objects as diverse as clouds and also aircraft. A Doppler shift in the radar echo can be supplied to identify the speed of a auto or the intensity of a rainstorm. Innovative radar systems are provided to map the Earth and also other planets, with a resolution minimal by wavelength. (See Figure 7.) The much shorter the wavelength of any kind of probe, the smaller sized the information it is feasible to observe.

Heating v Microwaves

How does the common microwave oven develop microwaves electronically, and why go food absorb castle preferentially? Microwaves at a frequency that 2.45 GHz are created by accelerating electrons. The microwaves are then offered to induce an alternate electric field in the oven.

Water and also some other constituents the food have actually a slightly negative charge at one end and also a slightly optimistic charge at one finish (called polar molecules). The range of microwave frequencies is specially selected so that the polar molecules, in do the efforts to store orienting themselves through the electrical field, absorb these energies and also increase their temperatures—called dielectric heating.

The energy thereby took in results in heat agitation heater food and also not the plate, i beg your pardon does not contain water. Hot spots in the food are pertained to constructive and also destructive interference patterns. Rotating antennas and also food turntables help spread the end the hot spots.

Another use of microwaves for heating is within the human being body. Microwaves will penetrate an ext than shorter wavelengths into tissue and also so can attain “deep heating” (called microwave diathermy). This is supplied for dealing with muscular pains, spasms, tendonitis, and rheumatoid arthritis.

Take-Home Experiment—Microwave Ovens

Look in ~ the door the a microwave oven. Define the structure of the door. Why is there a steel grid on the door? just how does the size of the holes in the grid compare through the wavelength of microwaves provided in microwave ovens? What is this wavelength?Place a glass that water (about 250 ml) in the microwave and heat it for 30 seconds. Measure the temperature acquire (the ΔT). Assuming that the power output the the stove is 1000 W, calculate the efficiency of the heat-transfer process.Remove the rotating turntable or relocating plate and also place a cup that water in several places along a line parallel v the opening. Warmth for 30 seconds and measure the ΔT because that each position. Carry out you see situations of disastrous interference?

Microwaves generated by atoms and also molecules much away with time and space can it is in received and also detected by digital circuits. Deep an are acts favor a blackbody with a 2.7 K temperature, radiating most of its energy in the microwave frequency range. In 1964, Penzias and also Wilson detected this radiation and eventually known that it to be the radiation the the huge Bang’s cooled remnants.

Infrared Radiation

The microwave and infrared areas of the electromagnetic spectrum overlap (see Figure 1). Infrared radiation is generally created by heat motion and also the vibration and rotation that atoms and molecules. Digital transitions in atoms and also molecules can also produce infrared radiation.

The range of infrared frequencies extends as much as the reduced limit of clearly shows light, just listed below red. In fact, infrared way “below red.” Frequencies in ~ its upper limit room too high to be created by speeding up electrons in circuits, but little systems, such as atoms and molecules, deserve to vibrate fast enough to create these waves.

Water molecule rotate and also vibrate particularly well in ~ infrared frequencies, emitting and absorbing them so successfully that the emissivity for skin is = 0.97 in the infrared. Night-vision scopes have the right to detect the infrared emitted by various warmth objects, including humans, and also convert the to visible light.

We deserve to examine radiant warm transfer indigenous a residence by utilizing a camera qualified of detecting infrared radiation. Enlightenment satellites can detect buildings, vehicles, and also even individual humans by their infrared emissions, whose strength radiation is proportional to the fourth power of the absolute temperature. More mundanely, we usage infrared lamps, several of which are referred to as quartz heaters, to preferentially warmth us since we absorb infrared much better than our surroundings.

The sunlight radiates choose a virtually perfect blackbody (that is, it has = 1), with a 6000 K surface ar temperature. About fifty percent of the solar energy showing up at the earth is in the infrared region, with many of the rest in the visible part of the spectrum, and a relatively small lot in the ultraviolet. ~ above average, 50 percent the the incident solar energy is took in by the Earth.

The relatively consistent temperature that the earth is a an outcome of the power balance between the incoming solar radiation and also the power radiated native the Earth. Many of the infrared radiation emitted from the planet is absorbed by CO2 and also H2O in the atmosphere and then radiated back to earth or into outer space. This radiation ago to planet is recognized as the greenhouse effect, and it maintains the surface temperature the the Earth around 40ºC greater than it would certainly be if there is no absorption. Some researchers think the the raised concentration of CO2 and also other greenhouse gases in the atmosphere, result from boosts in fossil fuel burning, has actually increased global average temperatures.

Visible Light

Visible light is the narrow segment that the electromagnetic spectrum to which the normal human eye responds. Visible irradiate is produced by vibrations and also rotations the atoms and also molecules, and by digital transitions in ~ atoms and molecules. The receivers or detectors that light mainly utilize electronic transitions. We say the atoms and molecules room excited once they absorb and relax when they emit through electronic transitions.

Figure 8 shows this part of the spectrum, in addition to the colors connected with certain pure wavelengths. Us usually describe visible irradiate as having wavelengths of in between 400 nm and 750 nm. (The retina of the eye actually responds to the shortest ultraviolet frequencies, but these do not generally reach the retina due to the fact that they are soaked up by the cornea and also lens the the eye.)

Red light has actually the shortest frequencies and also longest wavelengths, when violet has actually the greatest frequencies and shortest wavelengths. Blackbody radiation from the sunlight peaks in the visible part of the spectrum yet is more intense in the red than in the violet, make the sun yellowish in appearance.


Figure 9. This map that ozone concentration over Antarctica in October 2011 reflects severe depletion suspected to be brought about by CFCs. Much less dramatic but much more general depletion has been it was observed over north latitudes, arguing the effect is global. With less ozone, much more ultraviolet radiation indigenous the sun reaches the surface, causing much more damage. (credit: NASA Ozone Watch)

The Cl atom climate catalyzes the breakdown of ozone as follows:

Cl + O3 → ClO + O2 and ClO + O3 → Cl + 2O2.

A solitary chlorine atom might destroy ozone molecules because that up to two years before being transported under to the surface. The CFCs are relatively stable and will contribute to ozone depletion for years to come. CFCs are found in refrigerants, air conditioning systems, foams, and aerosols.

International concern over this trouble led come the establishment of the “Montreal Protocol” commitment (1987) to phase out CFC manufacturing in most countries. However, developing-country joining is essential if an international production and also elimination the CFCs is to be achieved. Most likely the biggest contributor to CFC emissions today is India. However the protocol appears to it is in working, together there are indications of one ozone recovery. (See Figure 9.)

Benefits the UV Light

Besides the adverse effects of ultraviolet radiation, over there are likewise benefits that exposure in nature and uses in technology. Vitamin D manufacturing in the skin (epidermis) outcomes from exposure to UVB radiation, usually from sunlight. A variety of studies indicate lack the vitamin D can result in the breakthrough of a range of cancers (prostate, breast, colon), therefore a specific amount of UV exposure is helpful. Lack of vitamin D is additionally linked to osteoporosis. Exposures (with no sunscreen) that 10 minutes a day to arms, face, and legs could be sufficient to provide the welcomed dietary level. However, in the winter time phibìc of around 37º latitude, many UVB gets clogged by the atmosphere.

UV radiation is supplied in the therapy of infantile jaundice and in some skin conditions. That is additionally used in sterilizing workspaces and also tools, and killing germs in a wide range of applications. That is likewise used together an analytical device to identify substances.

When exposed come ultraviolet, some substances, such together minerals, bright in characteristic clearly shows wavelengths, a process called fluorescence. So-called black color lights emit ultraviolet to reason posters and clothing come fluoresce in the visible. Ultraviolet is likewise used in special microscopes come detect details smaller sized than those observable with longer-wavelength visible-light microscopes.


Figure 11. Artist’s conception of one electron being slowed through collisions in a material and also emitting X-ray radiation. This energetic electron makes countless collisions with electrons and also atoms in a product it penetrates. An accelerated charge radiates EM waves, a second technique by i m sorry X-rays room created.

The second technique by i m sorry an energetic electron creates an X-ray when it strikes a material is shown in Figure 11. The electron interacts through charges in the material as it penetrates. These collisions deliver kinetic power from the electron come the electrons and also atoms in the material.

A loss of kinetic power implies an acceleration, in this situation decreasing the electron’s velocity. Whenever a charge is accelerated, that radiates EM waves. Offered the high energy of the electron, these EM waves can have high energy. We call them X-rays. Due to the fact that the process is random, a vast spectrum of X-ray power is emitted that is an ext characteristic the the electron energy than the type of material the electron encounters. Together EM radiation is dubbed “bremsstrahlung” (German because that “braking radiation”).


In the 1850s, researchers (such together Faraday) started experimenting through high-voltage electric discharges in tubes filled with rarefied gases. It was later discovered that this discharges created an invisible, penetrating type of an extremely high frequency electromagnetic radiation. This radiation was called an X-ray, because its identity and also nature to be unknown.

As described in “Things good and Small” feature, there space two methods through which X-rays space created—both space submicroscopic processes and also can be caused by high-voltage discharges. When the low-frequency end of the X-ray variety overlaps through the ultraviolet, X-rays expand to much greater frequencies (and energies).

X-rays have actually adverse impacts on life cells comparable to those that ultraviolet radiation, and they have actually the extr liability that being an ext penetrating, affecting more than the surface layers that cells. Cancer and genetic defects can be induced by exposure to X-rays. Due to the fact that of their effect on rapidly splitting cells, X-rays can likewise be offered to treat and even cure cancer.

The widest use of X-rays is because that imaging objects that are opaque to visible light, such together the person body or aircraft parts. In humans, the threat of cell damages is weighed carefully against the advantage of the diagnostic information obtained. However, questions have risen in recent years as to accidental overexposure the some world during CT scans—a mistake at least in component due to bad monitoring that radiation dose.

The capacity of X-rays come penetrate matter depends ~ above density, and so one X-ray image can reveal an extremely detailed density information. Figure 12 shows an example of the simplest form of X-ray image, one X-ray zero on film. The quantity of info in a basic X-ray picture is impressive, but more sophisticated techniques, such as CT scans, have the right to reveal three-dimensional info with details smaller sized than a millimeter.


Figure 13. This is picture of the γ-rays emitted through nuclei in a compound that is focused in the bones and also eliminated through the kidneys. Bone cancer is confirmed by nonuniform concentration in comparable structures. For example, part ribs room darker 보다 others. (credit: P. P. Urone)

Soon after nuclear radioactivity was first detected in 1896, that was uncovered that at the very least three distinct types of radiation to be being emitted. The many penetrating atom radiation was referred to as a gamma ray (γ ray) (again a surname given since its identity and also character were unknown), and it was later found to be really high frequency electromagnetic wave.

In fact, γ beam are any type of electromagnetic radiation emitted by a nucleus. This have the right to be from natural nuclear degeneration or induced nuclear processes in nuclear reactors and also weapons. The lower end of the γ-ray frequency selection overlaps the upper end of the X-ray range, however γ rays can have the highest frequency of any electromagnetic radiation.

Gamma rays have features identical come X-rays the the same frequency—they differ just in source. At higher frequencies, γ beam are more penetrating and more damaging to life tissue. Castle have many of the same supplies as X-rays, including cancer therapy. Gamma radiation from radioactive materials is offered in atom medicine.

Figure 13 shows a medical image based upon γ rays. Food spoilage deserve to be greatly inhibited by exposing it to huge doses that γ radiation, in order to obliterating responsible microorganisms. Damages to food cells through irradiation occurs as well, and the long-term perils of spend radiation-preserved food space unknown and also controversial for part groups. Both X-ray and γ-ray technologies are additionally used in scanning luggage in ~ airports.

Detecting Electromagnetic waves from Space

A final note top top star gazing. The entire electromagnetic spectrum is supplied by researchers for investigate stars, space, and time. As provided earlier, Penzias and Wilson detect microwaves to identify the elevator radiation originating native the large Bang. Radio telescopes such as the Arecibo Radio Telescope in Puerto Rico and also Parkes Observatory in Australia were designed to detect radio waves.

Infrared telescopes need to have actually their detectors cooled by fluid nitrogen to be able to gather useful signals. Because infrared radiation is mainly from heat agitation, if the detectors were not cooled, the vibrations that the molecules in the antenna would certainly be stronger than the signal being collected.

The most renowned of this infrared perceptible telescopes is the James salesman Maxwell Telescope in Hawaii. The more quickly telescopes, arisen in the seventeenth century, to be optical telescopes, collecting visible light. Telescopes in the ultraviolet, X-ray, and also γ-ray regions are placed external the atmosphere on satellites orbiting the Earth.

The Hubble room Telescope (launched in 1990) gathers ultraviolet radiation and visible light. In the X-ray region, there is the Chandra X-ray Observatory (launched in 1999), and also in the γ-ray region, there is the brand-new Fermi Gamma-ray room Telescope (launched in 2008—taking the location of the Compton Gamma ray Observatory, 1991–2000.).

PhET Explorations: shade Vision

Make a totality rainbow by mixing red, green, and also blue light. Change the wavelength of a monochromatic beam or filter white light. View the light as a heavy beam, or view the individual photons.


Click to operation the simulation.

Section Summary

The relationship amongst the rate of propagation, wavelength, and also frequency for any wave is provided by vW = , so that for electromagnetic waves, = , where f is the frequency, λ is the wavelength, and also c is the rate of light.The electromagnetic spectrum is separated into countless categories and subcategories, based on the frequency and also wavelength, source, and also uses of the electromagnetic waves.Any electromagnetic wave created by currents in wires is classified together a radio wave, the shortest frequency electromagnetic waves. Radio waves are separated into numerous types, depending upon their applications, ranging up to microwaves at their highest frequencies.Infrared radiation lies below visible light in frequency and is produced by heat motion and also the vibration and rotation of atoms and molecules. Infrared’s lower frequencies overlap through the highest-frequency microwaves.Visible light is largely developed by electronic transitions in atoms and molecules, and is characterized as being detectable through the human being eye. Its colors vary through frequency, indigenous red in ~ the lowest to violet at the highest.Ultraviolet radiation starts with frequencies just over violet in the visible range and is developed primarily by digital transitions in atoms and also molecules.X-rays are produced in high-voltage discharges and by electron bombardment of metal targets. Your lowest frequencies overlap the ultraviolet range but extend to much higher values, overlapping at the high finish with gamma rays.Gamma rays room nuclear in origin and are defined to incorporate the highest-frequency electromagnetic radiation of any kind of type.

Conceptual Questions

If you live in a an ar that has actually a specific TV station, you deserve to sometimes choose up few of its audio part on her FM radio receiver. Define how this is possible. Does it indicate that TV audio is broadcast together FM?Explain why people who have the lens of their eye removed since of cataracts room able to check out low-frequency ultraviolet.How carry out fluorescent soap residual water make clothes look “brighter and also whiter” in the end light? would this be effective in candlelight?Give an instance of resonance in the reception of electromagnetic waves.Illustrate the the size of details of an object that deserve to be detected through electromagnetic tide is pertained to their wavelength, by comparing details observable v two different types (for example, radar and also visible light or infrared and X-rays).Why don’t buildings block radio tide as completely as they perform visible light?Make a list of some everyday objects and decide even if it is they are transparent or opaque to each of the species of electromagnetic waves.Your friend states that more patterns and colors deserve to be viewed on the wings of birds if viewed in ultraviolet light. Would you agree v your friend? explain your answer.The price at which information deserve to be transmitted on an electromagnetic wave is proportional come the frequency of the wave. Is this regular with the truth that laser telephone infection at clearly shows frequencies dead far much more conversations every optical fiber 보다 conventional electronic transmission in a wire? What is the implication for ELF radio communication with submarines?Give an example of energy brought by one electromagnetic wave.In an MRI scan, a higher magnetic field requires greater frequency radio waves to resonate through the nuclear type whose density and also location is being imaged. What effect does going to a bigger magnetic field have on the most efficient antenna to transfer those radio waves? does it donate a smaller sized or larger antenna?Laser vision correction frequently uses an excimer laser the produces 193-nm electromagnetic radiation. This wavelength is incredibly strongly soaked up by the cornea and also ablates that in a manner the reshapes the cornea to exactly vision defects. Define how the solid absorption helps concentration the power in a slim layer and thus give greater accuracy in shaping the cornea. Additionally explain how this solid absorption borders damage come the lens and also retina the the eye.

Problems & Exercises

(a) 2 microwave frequencies space authorized for use in microwave ovens: 900 and also 2560 MHz. Calculation the wavelength that each. (b) i m sorry frequency would create smaller warm spots in foods due to interference effects?(a) calculation the range of wavelengths for AM radio provided its frequency range is 540 come 1600 kHz. (b) do the very same for the FM frequency variety of 88.0 come 108 MHz.A radio station utilizes frequencies in between commercial AM and FM. What is the frequency the a 11.12-m-wavelength channel?Find the frequency selection of visible light, given that it includes wavelengths indigenous 380 to 760 nm.Combing your hair leader to excess electron on the comb. How rapid would you have to move the comb up and also down to produce red light?Electromagnetic radiation having a 15.0−μm wavelength is classified as infrared radiation. What is the frequency?Approximately what is the smallest detail observable v a microscopic lense that offers ultraviolet irradiate of frequency 1.20 × 1015 Hz?A radar supplied to finding the presence of aircraft receives a pulse that has actually reflected off things 6 × 10−5 s ~ it was transmitted. What is the street from the radar terminal to the showing object?Some radar solution detect the size and also shape that objects such as aircraft and geological terrain. About what is the the smallest observable detail utilizing 500-MHz radar?Determine the quantity of time it takes because that X-rays that frequency 3 × 1018 Hz to travel (a) 1 mm and also (b) 1 cm.If you wish to detect details the the size of atoms (about 1 × 10−10 m) v electromagnetic radiation, the must have actually a wavelength of about this size. (a) What is that is frequency? (b) What type of electromagnetic radiation can this be?If the sunlight suddenly rotate off, we would not recognize it until its light quit coming. How long would that be, offered that the sun is 1.50 × 1011 m away?Distances in an are are often quoted in devices of irradiate years, the distance light travel in one year. (a) How many meters is a light year? (b) How plenty of meters is it come Andromeda, the nearest large galaxy, provided that the is 2.00 × 106 irradiate years away? (c) The most far-off galaxy yet uncovered is 12.0 × 109 irradiate years away. How far is this in meters?A particular 50.0-Hz AC power line radiates one electromagnetic wave having actually a maximum electric field strength of 13.0 kV/m. (a) What is the wavelength that this very low frequency electromagnetic wave? (b) What is its maximum magnetic field strength?During normal beating, the heart creates a maximum 4.00-mV potential throughout 0.300 m that a person’s chest, developing a 1.00-Hz electromagnetic wave. (a) What is the maximum electrical field toughness created? (b) What is the equivalent maximum magnetic field strength in the electromagnetic wave? (c) What is the wavelength the the electromagnetic wave?(a) The ideal size (most efficient) for a broadcast antenna with one end on the soil is one-fourth the wavelength \\left(\\frac\\lambda4\\right)\\\\ the the electromagnetic radiation being sent out. If a brand-new radio station has actually such an antenna that is 50.0 m high, what frequency does the broadcast many efficiently? Is this in the to be or FM band? (b) talk about the analogy the the an essential resonant setting of one air tower closed in ~ one finish to the resonance the currents on one antenna that is one-fourth their wavelength.(a) What is the wavelength of 100-MHz radio waves offered in an MRI unit? (b) If the frequencies room swept over a±1.00 selection centered ~ above 100 MHz, what is the range of wavelength broadcast?(a) What is the frequency that the 193-nm ultraviolet radiation provided in laser eye surgery? (b) presume the accuracy with which this EM radiation deserve to ablate the cornea is straight proportional come wavelength, exactly how much more accurate can this UV be than the shortest visible wavelength the light?TV-reception antennas because that VHF are created with cross wires supported at their centers, as displayed in . The ideal length for the overcome wires is one-half the wavelength to it is in received, with the an ext expensive antennas having one for each channel. Mean you measure up the lengths that the wires for specific channels and also find lock to be 1.94 and also 0.753 m long, respectively. What are the frequencies for these channels?

Figure 14. A television reception antenna has cross wires of various lengths come most efficiently receive different wavelengths.

Conversations v astronauts ~ above lunar walks had actually an echo the was supplied to estimate the distance to the Moon. The sound talked by the person on planet was transformed into a radio signal sent to the Moon, and also transformed earlier into sound top top a speaker within the astronaut’s room suit. This sound to be picked increase by the microphone in the room suit (intended because that the astronaut’s voice) and also sent back to planet as a radio echo the sorts. If the round-trip time was 2.60 s, what to be the approximate street to the Moon, neglecting any type of delays in the electronics?Lunar astronauts put a reflector top top the Moon’s surface, turn off which a laser beam is periodically reflected. The street to the Moon is calculated from the round-trip time. (a) to what accuracy in meters deserve to the distance to the Moon be determined, if this time can be measured come 0.100 ns? (b) What percent accuracy is this, given the typical distance come the Moon is 3.84 × 108 m?Radar is supplied to determine distances to various objects by measure the round-trip time for an echo native the object. (a) How far away is the planet Venus if the echo time is 1000 s? (b) What is the echo time because that a automobile 75.0 m native a Highway Police radar unit? (c) just how accurately (in nanoseconds) must you have the ability to measure the echo time come an plane 12.0 kilometres away to identify its distance within 10.0 m?Integrated Concepts. (a) calculation the proportion of the highest possible to lowest frequencies of electromagnetic tide the eye deserve to see, provided the wavelength variety of visible light is native 380 come 760 nm. (b) to compare this with the proportion of greatest to shortest frequencies the ear have the right to hear.Integrated Concepts. (a) calculate the rate in watts at which warm transfer v radiation occurs (almost entirely in the infrared) from 1.0 m2 the the Earth’s surface at night. I think the emissivity is 0.90, the temperature that the planet is 15ºC, and that that outer room is 2.7 K. (b) to compare the intensity of this radiation v that coming to the planet from the Sun during the day, which averages around 800 W/m2, only half of which is absorbed. (c) What is the best magnetic field strength in the outgoing radiation, assuming that is a continuous wave?


electromagnetic spectrum: the full range of wavelengths or frequencies the electromagnetic radiation

radio waves: electromagnetic waves v wavelengths in the selection from 1 mm to 100 km; they are produced by currents in wires and circuits and by expensive phenomena

microwaves: electromagnetic waves through wavelengths in the range from 1 mm to 1 m; they deserve to be created by currents in macroscopic circuits and devices

thermal agitation: the thermal motion of atoms and also molecules in any object at a temperature above absolute zero, which reasons them come emit and absorb radiation

radar: a common application that microwaves. Radar can determine the distance to objects as diverse as clouds and also aircraft, as well as determine the rate of a auto or the strongness of a rainstorm

infrared radiation (IR): a an ar of the electromagnetic spectrum with a frequency selection that extends from just below the red an ar of the visible irradiate spectrum approximately the microwave region, or from 0.74μm to 300μm

ultraviolet radiation (UV): electromagnetic radiation in the range extending increase in frequency native violet light and also overlapping with the lowest X-ray frequencies, through wavelengths indigenous 400 nm down to around 10 nm

visible light: the small segment that the electromagnetic spectrum to which the normal person eye responds

amplitude modulation (AM): a method for placing details on electromagnetic tide by modulating the amplitude of a transport wave v an audio signal, causing a wave with constant frequency but varying amplitude

extremely low frequency (ELF): electromagnetic radiation with wavelengths generally in the range of 0 to 300 Hz, but also around 1kHz

carrier wave: an electromagnetic tide that tote a signal through modulation of its amplitude or frequency

frequency modulation (FM): a technique of placing details on electromagnetic waves by modulating the frequency of a carrier wave with an audio signal, creating a wave of continuous amplitude however varying frequency

TV: video and audio signals transfer on electromagnetic waves

very high frequency (VHF): TV channels utilizing frequencies in the two arrays of 54 come 88 MHz and also 174 come 222 MHz

ultra-high frequency (UHF): TV channels in one even higher frequency variety than VHF, of 470 to 1000 MHz

X-ray: invisible, penetrating form of really high frequency electromagnetic radiation, overlapping both the ultraviolet variety and the γ-ray range

gamma ray: (γ ray); exceptionally high frequency electromagnetic radiation emitted by the nucleus of an atom, either from herbal nuclear degeneration or induced nuclear procedures in atom reactors and also weapons. The lower finish of the γ-ray frequency selection overlaps the upper finish of the X-ray range, but γ rays have the right to have the highest frequency of any kind of electromagnetic radiation

Selected services to Problems & Exercises

1. (a) 33.3 cm (900 MHz) 11.7 centimeter (2560 MHz); (b) The microwave cooktop with the smaller sized wavelength would develop smaller hot spots in foods, equivalent to the one v the frequency 2560 MHz.

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3. 26.96 MHz

5. 5.0 × 1014 Hz

7. \\lambda =\\fraccf=\\frac3\\text.\\text00\\times \\text10^8\\text m/s1\\text.\\text20\\times \\text10^\\text15\\text Hz=2\\text.\\text50\\times \\text10^-7\\text m\\\\

9. 0.600 m

11. (a) f=\\fracc\\lambda =\\frac3\\text.\\text00\\times \\text10^8\\text m/s1\\times \\text10^-\\text10\\text m=3\\times \\text10^\\text18\\text Hz\\\\; (b) X-rays

14. (a) 6.00 × 106 m; (b) 4.33 × 10−5 T

16. (a) 1.50 × 10 6 Hz, am band; (b) The resonance of currents on one antenna the is 1/4 your wavelength is analogous to the basic resonant setting of one air pillar closed in ~ one end, due to the fact that the tube also has a size equal to 1/4 the wavelength of the fundamental oscillation.

18. (a) 1.55 × 1015 Hz; (b) The shortest wavelength of visible light is 380 nm, for this reason that

\\beginarrayll\\text &\\frac\\lambda _\\textvisible\\lambda _\\textUV\\\\\\text =&\\frac380\\text nm193\\text nm\\\\\\text =&1.97\\endarray\\\\

In various other words, the UV radiation is 97% more accurate 보다 the shortest wavelength of visible light, or nearly twice as accurate!