Ch. 31 - Maxwell's Equations and Electromagnetic Waves

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 31 - Maxwell's Equations and Electromagnetic Waves

Problem 60

Chapter 30, Problem 60

What length of antenna would be appropriate for a portable device that could receive satellite TV?

Verified step by step guidance

Determine the frequency of the satellite TV signal. Satellite TV typically operates in the Ku-band, which ranges from 12 GHz to 18 GHz. For this problem, assume a specific frequency within this range, such as 15 GHz.

Calculate the wavelength of the signal using the formula:

λ = \frac{c}{f}

, where

c

is the speed of light (approximately 3 × 10⁸ m/s) and

f

is the frequency of the signal.

Substitute the values for

c

and

f

into the formula to find the wavelength

λ

. For example, if

f

= 15 GHz, calculate

λ

Determine the appropriate antenna length. For efficient reception, the antenna length is typically a fraction of the wavelength, such as

\frac{1}{4}

\frac{1}{2}

of the wavelength. Decide on the fraction based on the design constraints of the portable device.

Multiply the calculated wavelength by the chosen fraction to determine the appropriate antenna length. This will give you the final length suitable for the portable device to receive satellite TV signals.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Wavelength

Wavelength is the distance between successive peaks of a wave, which is crucial in determining the size of an antenna. For satellite TV, the wavelength of the signals being received typically falls within the microwave range, which is around 1 to 12 centimeters. The length of the antenna is often a fraction of the wavelength, commonly a quarter or half, to ensure efficient reception.

Antenna Design

Antenna design involves the shape and size of the antenna, which affects its ability to receive specific frequencies. Different designs, such as dipole or parabolic antennas, are optimized for various applications. For satellite TV, a parabolic dish is often used to focus signals, while portable devices may utilize compact designs that balance size and performance.

Frequency Band

The frequency band refers to the range of electromagnetic frequencies used for communication. Satellite TV typically operates in the Ku-band (12 to 18 GHz) or Ka-band (26.5 to 40 GHz). Understanding the frequency band is essential for selecting an appropriate antenna length, as it directly influences the wavelength and, consequently, the antenna's dimensions.

Recommended video:

Guided course

05:08

Circumference, Period, and Frequency in UCM

Related Practice

Textbook Question

A global positioning system (GPS) functions by determining the travel times for EM waves from various satellites to a moving GPS receiver on Earth (car or hiker). If the receiver is to detect a change in the receiver’s position on the order of 3 m, what is the associated change in travel time (in ns) that must be measured?

Textbook Question

What is the maximum power level of a radio station so as to avoid electrical breakdown of air at a distance of 0.75 m from the transmitting antenna? Assume the antenna is a point source. Air breaks down in an electric field of about 3 x 10⁶ V/m.

views

Textbook Question

Show that displacement current, ε₀ (dΦE/dt), has the SI units of amperes.

views

Textbook Question

Radio-controlled clocks throughout the United States receive a radio signal from a transmitter in Fort Collins, Colorado, that accurately (within a microsecond) marks the beginning of each minute. A slight amount of time is added by a clock at any location to correct for the signal travel time to the clock from Fort Collins. Assuming Fort Collins is no more than 3000 km from any point in the U.S., what is the longest travel-time delay?

Textbook Question

A powerful laser portrayed in a movie provides a 3-mm-diameter beam of green light with a power of 3 W. A good agent inside a spacecraft aims the laser beam at an enemy astronaut hovering outside. The mass of the enemy astronaut is 120 kg and the spacecraft 185,000 kg. (a) Determine the “radiation-pressure” force exerted on the enemy by the laser beam assuming her suit is perfectly reflecting. (b) If the enemy is 30 m from the spacecraft’s center of mass, estimate the gravitational force the spacecraft exerts on the enemy. (c) Which of the two forces is larger, and by what factor?

views

Textbook Question

The average intensity of a particular TV station’s signal is 1.0 x 10^-13 W/m² when it arrives at a 33-cm-diameter satellite TV antenna. (a) Calculate the total energy received by the antenna during 3.0 hours of viewing this station’s programs. (b) Estimate the amplitudes of the E and B fields of the EM wave.