In astronomy, distances are often expressed in

The team monitoring a space probe exploring the outer solar system fi nds that radio transmissions from the probe take 2.53 hours to reach earth. How distant (in meters) is the probe?

(a) Neil A. Armstrong was the fi rst person to walk on the moon. The distance between the earth and the moon is 3.85 3 108 m. Find the time it took for his voice to reach the earth via radio waves. (b) Someday a person will walk on Mars, which is 5.6 3 1010 m from the earth at the point of closest approach. Determine the minimum time that will be required for a message from Mars to reach the earth via radio waves.

In astronomy, distances are often expressed in light-years. One light-year is the distance traveled by light in one year. The distance to Alpha Centauri, the closest star other than our own sun that can be seen by the naked eye, is 4.3 light-years. Express this distance in meters

FM radio stations use radio waves with frequencies from 88.0 to 108 MHz to broadcast their signals. Assuming that the inductance in Figure 24.4 has a value of 6.00 3 1027 H, determine the range of capacitance values that are needed so the antenna can pick up all the radio waves broadcasted by FM stations.

In a traveling electromagnetic wave, the electric fi eld is represented mathematically as E 5 E0 sin [(1.5 3 1010 s21 )t 2 (5.0 3 101 m21 )x] where E0 is the maximum fi eld strength. This equation is an adaptation of Equation 16.3. (a) What is the frequency of the wave? (b) This wave and the wave that results from its refl ection can form a standing wave, in a way similar to that in which standing waves can arise on a string (see Section 17.5). What is the separation between adjacent nodes in the standing wave?

A fl at coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.25 m and consists of 450 turns. The transmitted radio wave has a frequency of 1.2 MHz. The magnetic fi eld of the wave is parallel to the normal to the coil and has a maximum value of 2.0 3 10213 T. Using Faradays law of electromagnetic induction and the fact that the magnetic fi eld changes from zero to its maximum value in one-quarter of a wave period, fi nd the magnitude of the average emf induced in the antenna during this time.

A truck driver is broadcasting at a frequency of 26.965 MHz with a CB (citizens band) radio. Determine the wavelength of the electromagnetic wave being used. The speed of light is c 5 2.9979 3 108 m/s.

In a dentists offi ce an X-ray of a tooth is taken using X-rays that have a frequency of 6.05 3 1018 Hz. What is the wavelength in vacuum of these X-rays?

In a certain UHF radio wave, the shortest distance between positions at which the electric and magnetic fi elds are zero is 0.34 m. Determine the frequency of this UHF radio wave.

FM radio waves have frequencies between 88.0 and 108.0 MHz. Determine the range of wavelengths for these waves.

Magnetic resonance imaging, or MRI (see Section 21.7), and positron emission tomography, or PET scanning (see * ** Section 32.6), are two medical diagnostic techniques. Both employ electromagnetic waves. For these waves, fi nd the ratio of the MRI wavelength (frequency 5 6.38 3 107 Hz) to the PET scanning wavelength (frequency 5 1.23 3 1020 Hz).

A certain type of laser emits light that has a frequency of 5.2 3 1014 Hz. The light, however, occurs as a series of short pulses, each lasting for a time of 2.7 3 10211 s. (a) How many wavelengths are there in one pulse? (b) The light enters a pool of water. The frequency of the light remains the same, but the speed of the light slows down to 2.3 3 108 m/s. How many wavelengths are there now in one pulse?

Two radio waves are used in the operation of a cellular telephone. To receive a call, the phone detects the wave emitted at one frequency by the transmitter station or base unit. To send your message to the base unit, your phone emits its own wave at a diff erent frequency. The diff erence between these two frequencies is fi xed for all channels of cell phone operation. Suppose that the wavelength of the wave emitted by the base unit is 0.34339 m and the wavelength of the wave emitted by the phone is 0.36205 m. Using a value of 2.9979 3 108 m/s for the speed of light, determine the diff erence between the two frequencies used in the operation of a cell phone.

A positively charged object with a mass of 0.115 kg oscillates at the end of a spring, generating ELF (extremely low frequency) radio waves that have a wavelength of 4.80 3 107 m. The frequency of these radio waves is the same as the frequency at which the object oscillates. What is the spring constant of the spring?

Review Conceptual Example 3 for information pertinent to this problem. When we look at the star Polaris (the North Star), we are seeing it as it was 680 years ago. How far away from us (in meters) is Polaris?

Figure 24.12 illustrates Michelsons setup for measuring the speed of light with the mirrors placed on Mt. San Antonio and Mt. Wilson in California, which are 35 km apart. Using a value of 3.00 3 108 m/s for the speed of light, fi nd the minimum angular speed (in rev/s) for the rotating mirror

Two astronauts are 1.5 m apart in their spaceship. One speaks to the other. The conversation is transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 343 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth. How far away from the earth is the spaceship?

A laptop computer communicates with a router wirelessly, by means of radio signals. The router is connected by cable directly to the Internet. The laptop is 8.1 m from the router, and is downloading text and images from the Internet at an average rate of 260 Mbps, or 260 megabits per second. (A bit, or binary digit, is the smallest unit of digital information.) On average, how many bits are downloaded to the laptop in the time it takes the wireless signal to travel from the router to the laptop?

A lidar (laser radar) gun is an alternative to the standard radar gun that uses the Doppler eff ect to catch speeders. A lidar gun uses an infrared laser and emits a precisely timed series of pulses of infrared electromagnetic waves. The time for each pulse to travel to the speeding vehicle and return to the gun is measured. In one situation a lidar gun in a stationary police car observes a diff erence of 1.27 3 1027 s in round-trip travel times for two pulses that are emitted 0.450 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

A politician holds a press conference that is televised live. The sound picked up by the microphone of a TV news network is broadcast via electromagnetic waves and heard by a television viewer. This viewer is seated 2.3 m from his television set. A reporter at the press conference is located 4.1 m from the politician, and the sound of the words travels directly from the celebritys mouth, through the air, and into the reporters ears. The reporter hears the words exactly at the same instant that the television viewer hears them. Using a value of 343 m/s for the speed of sound, determine the maximum distance between the television set and the politician. Ignore the small distance between the politician and the microphone. In addition, assume that the only delay between what the microphone picks up and the sound being emitted by the television set is that due to the travel time of the electromagnetic waves used by the network

A mirror faces a cliff located some distance away. Mounted on the cliff is a second mirror, directly opposite the fi rst mirror and facing toward it. A gun is fi red very close to the fi rst mirror. The speed of sound is 343 m/s. How many times does the fl ash of the gunshot travel the roundtrip distance between the mirrors before the echo of the gunshot is heard?

A laser emits a narrow beam of light. The radius of the beam is 1.0 3 1023 m, and the power is 1.2 3 1023 W. What is the intensity of the laser beam?

An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is S 5 1.23 3 109 W/m2 . What is the rms value of (a) the electric fi eld and (b) the magnetic fi eld in the electromagnetic wave emitted by the laser?

The maximum strength of the magnetic fi eld in an electromagnetic wave is 3.3 3 1026 T. What is the maximum strength of the waves electric fi eld?

The microwave radiation left over from the Big Bang explosion of the universe has an average energy density of 4 3 10214 J/m3 . What is the rms value of the electric fi eld of this radiation?

On a cloudless day, the sunlight that reaches the surface of the earth has an intensity of about 1.0 3 103 W/m2 . What is the electromagnetic energy contained in 5.5 m3 of space just above the earths surface?

Multiple-Concept Example 5 discusses the principles used in this problem. A neodymium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric fi eld of such a wave has an rms value of Erms 5 2.0 3 109 N/C. Find the average power of each pulse that passes through a 1.6 3 1025 -m2 surface that is perpendicular to the laser beam.

Consult Multiple-Concept Example 5 to review the concepts on which this problem depends. A light bulb emits light uniformly in all directions. The average emitted power is 150.0 W. At a distance of 5.00 m from the bulb, determine (a) the average intensity of the light, (b) the rms value of the electric fi eld, and (c) the peak value of the electric fi eld

Multiple-Concept Example 5 provides some pertinent background for this problem. The mean distance between earth and the sun is 1.50 3 1011 m. The average intensity of solar radiation incident on the upper atmosphere of the earth is 1390 W/m2 . Assuming that the sun emits radiation uniformly in all directions, determine the total power radiated by the sun.

A stationary particle of charge q 5 2.6 3 1028 C is placed in a laser beam (an electromagnetic wave) whose intensity is 2.5 3 103 W/m2 . Determine the magnitudes of the (a) electric and (b) magnetic forces exerted on the charge. If the charge is moving at a speed of 3.7 3 104 m/s perpendicular to the magnetic fi eld of the electromagnetic wave, fi nd the magnitudes of the (c) electric and (d) magnetic forces exerted on the particle.

The power radiated by the sun is 3.9 3 1026 W. The earth orbits the sun in a nearly circular orbit of radius 1.5 3 1011 m. The earths axis of rotation is tilted by 278 relative to the plane of the orbit (see the drawing), so sunlight does not strike the equator perpendicularly. What power strikes a 0.75-m2 patch of fl at land at the equator at point Q?

An electromagnetic wave strikes a 1.30-cm2 section of wall perpendicularly. The rms value of the waves magnetic fi eld is determined to be 6.80 3 1024 T. How long does it take for the wave to deliver 1850 J of energy to the wall?

A heat lamp emits infrared radiation whose rms electric fi eld is Erms 5 2800 N/C. (a) What is the average intensity of the radiation? (b) The radiation is focused on a persons leg over a circular area of radius 4.0 cm. What is the average power delivered to the leg? (c) The portion of the leg being irradiated has a mass of 0.28 kg and a specifi c heat capacity of 3500 J/(kg ? C8). How long does it take to raise its temperature by 2.0 C8? Assume that there is no other heat transfer into or out of the portion of the leg being heated.

A gamma-ray telescope intercepts a pulse of gamma radiation from a magnetar, a type of star with a spectacularly large magnetic fi eld. The pulse lasts 0.24 s and delivers 8.4 3 1026 J of energy perpendicularly to the 75-m2 surface area of the telescopes detector. The magnetar is thought to be 4.5 3 1020 m (about 50 000 light-years) from earth, and to have a radius of 9.0 3 103 m. Find the magnitude of the rms magnetic fi eld of the gamma-ray pulse at the surface of the magnetar, assuming that the pulse radiates uniformly outward in all directions.

A distant galaxy emits light that has a wavelength of 434.1 nm. On earth, the wavelength of this light is measured to be 438.6 nm. (a) Decide whether this galaxy is approaching or receding from the earth. Give your reasoning. (b) Find the speed of the galaxy relative to the earth.

A speeder is pulling directly away and increasing his distance from a police car that is moving at 25 m/s with respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 7.0 3 109 Hz. The wave refl ects from the speeders car and returns to the police car, where its frequency is measured to be 320 Hz less than the emitted frequency. Find the speeders speed with respect to the ground.

A distant galaxy is simultaneously rotating and receding from the earth. As the drawing shows, the galactic center is receding from the earth at a relative speed of uG 5 1.6 3 106 m/s. Relative to the center, the tangential speed is vT 5 0.4 3 106 m/s for locations A and B, which are equidistant from the center. When the frequencies of the light coming from regions A and B are measured on earth, they are not the same and each is diff erent from the emitted frequency of 6.200 3 1014 Hz. Find the measured frequency for the light from (a) region A and (b) region B.

The drawing shows three situationsA, B, and Cin which an observer and a source of electromagnetic waves are moving along the same line. In each case the source emits a wave that has a frequency of 4.57 3 1014 Hz. The arrows in each situation denote velocity vectors of the observer and source relative to the ground and have the magnitudes indicated (v or 2v), where the speed v is 1.50 3 106 m/s. Calculate the observed frequency in each of the three cases.

Unpolarized light whose intensity is 1.10 W/m2 is incident on the polarizer in Figure 24.20. (a) What is the intensity of the light leaving the polarizer? (b) If the analyzer is set at an angle of u 5 758 with respect to the polarizer, what is the intensity of the light that reaches the photocell?

The drawing shows three polarizer/analyzer pairs. The incident light beam for each pair is unpolarized and has the same average intensity of 48 W/m2 . Find the average intensity of the transmitted beam for each of the three cases (A, B, and C) shown in the drawing.

The average intensity of light emerging from a polarizing sheet is 0.764 W/m2 , and the average intensity of the horizontally polarized light incident on the sheet is 0.883 W/m2 . Determine the angle that the transmission axis of the polarizing sheet makes with the horizontal.

Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 94% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes through the second sheet. What angle does the transmission axis of the second sheet make with the vertical?

Review Conceptual Example 7 before solving this problem. Suppose that unpolarized light of intensity 150 W/m2 falls on the polarizer in Figure 24.23a, and the angle u in the drawing is 30.08. What is the light intensity reaching the photocell?

The drawing shows light incident on a polarizer whose transmission axis is parallel to the z axis. The polarizer is rotated clockwise through an angle a. The average intensity of the incident light is 7.0 W/m2 . Determine the average intensity of the transmitted light for each of the six cases shown in the table.

For each of the three sheets of polarizing material shown in the drawing, the orientation of the transmission axis is labeled relative to the vertical. The incident beam of light is unpolarized and has an intensity of 1260.0 W/m2 . What is the intensity of the beam transmitted through the three sheets when u1 5 19.08, u2 5 55.08, and u3 5 100.08?

Before attempting this problem, review Conceptual Example 7. The intensity of the light that reaches the photocell in Figure 24.23a is 110 W/m2 , when u 5 238. What would be the intensity reaching the photocell if the analyzer were removed from the setup, everything else remaining the same?

More than one analyzer can be used in a setup like the one in Figure 24.20, each analyzer following the previous one. Suppose that the transmission axis of the fi rst analyzer is rotated 278 relative to the transmission axis of the polarizer, and that the transmission axis of each additional analyzer is rotated 278 relative to the transmission axis of the previous one. What is the minimum number of analyzers needed for the light reaching the photocell to have an intensity that is reduced by at least a factor of 100 relative to the intensity of the light striking the fi rst analyzer?

The drawing shows four sheets of polarizing material, each with its transmission axis oriented diff erently. Light that is polarized in the vertical direction is incident from the left and has an average intensity of 27 W/m2 . Determine the average intensity of the light that emerges on the right in the drawing when sheet A alone is removed, when sheet B alone is removed, when sheet C alone is removed, and when sheet D alone is removed.

Obtain the wavelengths in vacuum for (a) blue light whose frequency is 6.34 3 1014 Hz, and (b) orange light whose frequency is 4.95 3 1014 Hz. Express your answers in nanometers (1 nm 5 1029 m).

The magnitude of the electric fi eld of an electromagnetic wave increases from 315 to 945 N/C. (a) Determine the wave intensities for the two values of the electric fi eld. (b) What is the magnitude of the magnetic fi eld associated with each electric fi eld? (c) Determine the wave intensity for each value of the magnetic fi eld.

An AM station is broadcasting a radio wave whose frequency is 1400 kHz. The value of the capacitance in Figure 24.4 is 8.4 3 10211 F. What must be the value of the inductance in order that this station can be tuned in by the radio?

The human eye is most sensitive to light with a frequency of about 5.5 3 1014 Hz, which is in the yellow-green region of the electromagnetic spectrum. How many wavelengths of this light can fi t across the width of your thumb, a distance of about 2.0 cm?

A future space station in orbit about the earth is being powered by an electromagnetic beam from the earth. The beam has a cross-sectional area of 135 m2 and transmits an average power of 1.20 3 104 W. What are the rms values of the (a) electric and (b) magnetic fi elds?

Suppose that a police car is moving to the right at 27 m/s, while a speeder is coming up from behind at a speed of 39 m/s, both speeds being with respect to the ground. Assume that the electromagnetic wave emitted by the police cars radar gun has a frequency of 8.0 3 109 Hz. Find the diff erence between the frequency of the wave that returns to the police car after refl ecting from the speeders car and the original frequency emitted by the police car.

In experiment 1, unpolarized light falls on the polarizer in Figure 24.20. The angle of the analyzer is u 5 60.08. In experiment 2, the unpolarized light is replaced by light of the same intensity, but the light is polarized along the direction of the polarizers transmission axis. By how many additional degrees must the analyzer be rotated so that the light falling on the photocell will have the same intensity as it did in experiment 1? Explain whether u is increased or decreased by this additional number of degrees.

The electromagnetic wave that delivers a cellular phone call to a car has a magnetic fi eld with an rms value of 1.5 3 10210 T. The wave passes perpendicularly through an open window, the area of which is 0.20 m2 . How much energy does this wave carry through the window during a 45-s phone call?

Equation 16.3, y 5 A sin (2pft 2 2px/l), gives the mathematical representation of a wave oscillating in the y direction and traveling in the positive x direction. Let y in this equation equal the electric fi eld of an electromagnetic wave traveling in a vacuum. The maximum electric fi eld is A 5 156 N/C, and the frequency is f 5 1.50 3 108 Hz. Plot a graph of * * the electric fi eld strength versus position, using for x the following values: 0, 0.50, 1.00, 1.50, and 2.00 m. Plot this graph for (a) a time t 5 0 s and (b) a time t that is one-fourth of the waves period.

A beam of polarized light with an average intensity of 15 W/m2 is sent through a polarizer. The transmission axis makes an angle of 258 with respect to the direction of polarization. Determine the rms value of the electric fi eld of the transmitted beam.

An argonion laser produces a cylindrical beam of light whose average power is 0.750 W. How much energy is contained in a 2.50-m length of the beam?

What fraction of the power radiated by the sun is intercepted by the planet Mercury? The radius of Mercury is 2.44 3 106 m, and its mean distance from the sun is 5.79 3 1010 m. Assume that the sun radiates uniformly in all directions.

The drawing shows an edge-on view of the solar panels on a communications satellite. The dashed line specifies the normal to the panels. Sunlight strikes the panels at an angle u with respect to the normal. If the solar power impinging on the panels is 2600 W when u 5 658, what is it when u 5 258?

Suppose that the light falling on the polarizer in Figure 24.20 is partially polarized (average intensity 5 SP) and partially unpolarized (average intensity 5 SU). The total incident intensity is SP 1 SU, and the percentage polarization is 100 SP /(SP 1 SU). When the polarizer is rotated in such a situation, the intensity reaching the photocell varies between a minimum value of Smin and a maximum value of Smax. Show that the percentage polarization can be expressed as 100 (Smax 2 Smin)/(Smax 1 Smin).

Police use radar guns and the Doppler eff ect to catch speeders. The fi gure illustrates a moving car approaching a stationary police car. A radar gun emits an electromagnetic wave that refl ects from the oncoming car. The refl ected wave returns to the police car with a frequency (measured by on-board equipment) that is diff erent from the emitted frequency. One such radar gun emits a wave whose frequency is 8.0 3 109 Hz. When the speed of the car is 39 m/s and the approach is essentially head-on, what is the diff erence between the frequency of the wave returning to the police car and that emitted by the radar gun?

The fi gure shows the popular dish antenna that receives digital TV signals from a satellite. The average intensity of the electromagnetic wave that carries a particular TV program is S 5 7.5 3 10214 W/m2 , and the circular aperture of the antenna has a radius of r 5 15 cm. Concepts: (i) How is the average power passing through the circular aperture of the antenna related to the average intensity of the TV signal? (ii) How much energy does the antenna receive in a time t? (iii) What is the average * energy density, or average energy per unit volume, of the electromagnetic wave? Calculations: (a) Determine the electromagnetic energy delivered to the dish during a one-hour program. (b) What is the average energy density of the electromagnetic wave?

The light beam in the fi gure passes through a polarizer whose transmission axis makes an angle f with the vertical. The beam is partially polarized and partially unpolarized, and the average intensity S0 of the incident light is the sum of the average intensity S0, polar of the polarized light and the average intensity S0, unpolar of the unpolarized light; S0 5 S0, polar 1 S0, unpolar. The intensity S of the transmitted light is also the sum of two parts: S 5 Spolar 1 Sunpolar. As the polarizer is rotated clockwise, the intensity of the transmitted light has a minimum value of S 5 2.0 W/m2 when f 5 20.0 and has a maximum value of S 5 8.0 W/m2 when the angle is f 5 fmax. Concepts: (i) How is Sunpolar related to S0, unpolar? (ii) How is Spolar related to S0, polar? (iii) The minimum transmitted intensity is 2.0 W/m2 . Why isnt it 0 W/m2 ? Calculations: (a) What is the intensity S0, unpolar of the incident light that is unpolarized? (b) What is the intensity S0, polar of the incident light that is polarized?