Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
ssm Solution is in the Student Solutions Manual.
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Section 24.1 The Nature of Electromagnetic Waves

| 1 | (a) Neil A. Armstrong was the first person to walk on the moon. The distance between the earth and the moon is . Find the time it took for his voice to reach earth via radio waves. (b) Someday a person will walk on Mars, which is from earth at the point of closest approach. Determine the minimum time that will be required for that person’s voice to reach earth.

| 2 | During a flare-up from a sunspot, X-rays (electromagnetic waves) are emitted. If the distance between the sun and the earth is , how long (in minutes) does it take for the X-rays to reach the earth?

| 3 | ssm 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.

| 4 | FM radio stations use radio waves with frequencies from 88.0 to 108 MHz to broadcast their signals. Assuming that the inductance in Figure 24-5 has a value of , determine the range of capacitance values that are needed so the antenna can pick up all the radio waves broadcasted by FM stations.

* | 5 | ssm Equation 16.3, , 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 field of an electromagnetic wave traveling in a vacuum. The maximum electric field is , and the frequency is . Plot a graph of the electric field 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 s and (b) a time t that is one-fourth of the wave’s period.

* | 6 | A flat 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 field of the wave is parallel to the normal to the coil and has a maximum value of T. Using Faraday’s law of electromagnetic induction and the fact that the magnetic field changes from zero to its maximum value in one-quarter of a wave period, find the magnitude of the average emf induced in the antenna during this time.
Section 24.2 The Electromagnetic Spectrum

| 7 | A truck driver is broadcasting at a frequency of 26.965 MHz with a CB (citizen’s band) radio. Determine the wavelength of the electromagnetic wave being used.

| 8 | Obtain the wavelengths in vacuum for (a) blue light whose frequency is Hz, and (b) orange light whose frequency is Hz. Express your answers in nanometers .

| 9 | ssm www At one time television sets used “rabbit-ears” antennas. Such an antenna consists of a pair of metal rods. The length of each rod can be adjusted to be one-quarter of a wavelength of an electromagnetic wave whose frequency is 60.0 MHz. How long is each rod?

| 10 | 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, find the ratio of the MRI wavelength to the PET scanning wavelength .

| 11 | ssm The human eye is most sensitive to light having a frequency of about , which is in the yellow-green region of the electromagnetic spectrum. How many wavelengths of this light can fit across the width of your thumb, a distance of about 2.0 cm?

| 12 | 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 different frequency. The difference between these two frequencies is fixed for all channels of cell phone operation. Suppose 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 for the speed of light, determine the difference between the two frequencies used in the operation of a cell phone.

* | 13 | Section 17.5 deals with transverse standing waves on a string. Electromagnetic waves also can form standing waves. In a standing wave pattern formed from microwaves, the distance between a node and an adjacent antinode is 0.50 cm. What is the microwave frequency?
Section 24.3 The Speed of Light

| 14 | 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?

| 15 | ssm 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 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?

| 16 | A lidar (laser radar) gun is an alternative to the standard radar gun that uses the Doppler effect to catch speeders. A lidar gun uses an in frared 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 difference of 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.

| 17 | Figure 24-12 illustrates Michelson’s 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 for the speed of light, find the minimum angular speed for the rotating mirror.

| 18 | A communications satellite is in a synchronous orbit that is directly above the equator. The satellite is located midway between Quito, Equador, and Belém, Brazil, two cities almost on the equator that are separated by a distance of . Find the time it takes for a telephone call to go by way of satellite between these cities. Ignore the curvature of the earth.

* | 19 | ssm A mirror faces a cliff located some distance away. Mounted on the cliff is a second mirror, directly opposite the first mirror and facing toward it. A gun is fired very close to the first mirror. The speed of sound is 343 m/s. How many times does the flash of the gunshot travel the round-trip distance between the mirrors before the echo of the gunshot is heard?

* | 20 | A celebrity holds a press conference, which is televised live. A television viewer hears the sound picked up by a microphone directly in front of the celebrity. This viewer is seated 2.3 m from the television set. A reporter at the press conference is located 4.1 m from the microphone and hears the words directly at the very 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 viewer and the celebrity.
Section 24.4 The Energy Carried by Electromagnetic Waves

| 21 | A laser emits a narrow beam of light. The radius of the beam is , and the power is . What is the intensity of the laser beam?

| 22 | An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is . What is the rms value of (a) the electric field and (b) the magnetic field in the electromagnetic wave emitted by the laser?

| 23 | ssm The microwave radiation left over from the Big Bang explosion of the universe has an average energy density of . What is the rms value of the electric field of this radiation?

| 24 | 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 field of such a wave has an rms value of . Find the average power of each pulse that passes through a surface that is perpendicular to the laser beam.

| 25 | ssm The average intensity of sunlight at the top of the earth’s atmosphere is . What is the maximum energy that a solar panel could collect in one hour in this sunlight?

| 26 | Multiple-Concept Example 5 provides some pertinent background for this problem. The mean distance between earth and the sun is . The average intensity of solar radiation incident on the upper atmosphere of the earth is . Assuming the sun emits radiation uniformly in all directions, determine the total power radiated by the sun.

* | 27 | An argon-ion 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?

* | 28 | An electromagnetic wave strikes a 1.30-cm2 section of wall perpendicularly. The rms value of the wave’s magnetic field is . How long does it take for the wave to deliver 1850 J of energy to the wall?

* | 29 | What fraction of the power radiated by the sun is intercepted by the planet Mercury? The radius of Mercury is , and its mean distance from the sun is . Assume that the sun radiates uniformly in all directions.

** | 30 | The average intensity of sunlight reaching the earth is . A charge of is placed in the path of this electromagnetic wave. (a) What is the magnitude of the maximum electric force that the charge experiences? (b) If the charge is moving at a speed of , what is the magnitude of the maximum magnetic force that the charge could experience?
Section 24.5 The Doppler Effect and Electromagnetic Waves

| 31 | Review Interactive Solution 24.31 at to see one model for solving this problem. 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.

| 32 | Multiple-Concept Example 6 reviews the concepts that play a role in this problem. 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 . The wave reflects from the speeder’s car and returns to the police car, where its frequency is measured to be 320 Hz less than the emitted frequency. Find the speeder’s speed with respect to the ground.

* | 33 | ssm 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 . Relative to the center, the tangential speed is 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 different from the emitted frequency of . Find the measured frequency for the light from (a) region A and (b) region B.

Section 24.6 Polarization

| 34 | Unpolarized light whose intensity is 1.10 W/m2 is incident on the polarizer in Figure 24-21. (a) What is the intensity of the light leaving the polarizer? (b) If the analyzer is set at an angle of with respect to the polarizer, what is the intensity of the light that reaches the photocell?

| 35 | ssm Linearly polarized light is incident on a piece of polarizing material. What is the ratio of the transmitted light intensity to the incident light intensity when the angle between the transmission axis and the incident electric field is (a) 25° and (b) 65°?

| 36 | For one approach to this problem, consult Interactive Learning-Ware 24.1 at . 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 , , and ?

| 37 | Review Conceptual Example 8 before solving this problem. Suppose unpolarized light of intensity 150 W/m2 falls on the polarizer in Figure 24-24a, and the angle in the drawing is 30.0°. What is the light intensity reaching the photocell?

| 38 | In experiment 1, unpolarized light falls on the polarizer in Figure 24-21. The angle of the analyzer is . In experiment 2, the unpolarized light is replaced by light of the same intensity, but the light is polarized along the direction of the polarizer’s 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 is increased or decreased by this additional rotation.

* | 39 | ssm www More than one analyzer can be used in a setup like that in Figure 24-21, each analyzer following the previous one. Suppose that the transmission axis of the first analyzer is rotated 27° relative to the transmission axis of the polarizer, and that the transmission axis of each additional analyzer is rotated 27° 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 that striking the first analyzer?

* | 40 | Before attempting this problem, review Conceptual Example 8. The intensity of the light that reaches the photocell in Figure 24-24a is 110 W/m2, when . What would be the intensity reaching the photocell if the analyzer were removed from the setup, everything else remaining the same?

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