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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
All textbooksGiancoli Douglas 5th editionCh. 31 - Maxwell's Equations and Electromagnetic WavesProblem 42
Chapter 30, Problem 42

Compare 1030 on the AM dial to 103.1 on FM. Which has the longer wavelength, and by what factor is it larger?

Verified step by step guidance
1
Understand the relationship between frequency and wavelength using the formula: λ=cf, where λ is the wavelength, c is the speed of light (approximately 3×10^8 m/s), and f is the frequency.
Convert the given frequencies into standard units (Hertz). For AM, 1030 on the AM dial corresponds to 1030 kHz, which is 1030×10^3 Hz. For FM, 103.1 on the FM dial corresponds to 103.1 MHz, which is 103.1×10^6 Hz.
Calculate the wavelength for each frequency using the formula λ=cf. For AM, substitute f=1030×10^3 Hz. For FM, substitute f=103.1×10^6 Hz.
Compare the wavelengths by dividing the AM wavelength by the FM wavelength. This will give the factor by which the AM wavelength is larger than the FM wavelength.
Conclude which frequency has the longer wavelength (AM or FM) and state the factor by which it is larger, based on the result of the division in the previous step.

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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, typically measured in meters. In the context of radio waves, longer wavelengths correspond to lower frequencies. The relationship between wavelength (λ) and frequency (f) is given by the equation λ = c/f, where c is the speed of light. Thus, understanding how to calculate wavelength from frequency is essential for comparing different radio signals.
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AM vs. FM Radio

AM (Amplitude Modulation) and FM (Frequency Modulation) are two methods of encoding information in radio waves. AM radio waves vary in amplitude, while FM radio waves vary in frequency. Generally, AM frequencies are lower than FM frequencies, leading to longer wavelengths for AM signals. This distinction is crucial for determining which signal has a longer wavelength based on their respective frequencies.
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Frequency and Wavelength Relationship

The frequency of a wave is inversely related to its wavelength. As frequency increases, wavelength decreases, and vice versa. This relationship is fundamental in understanding radio waves, where AM stations typically operate at lower frequencies (and thus longer wavelengths) compared to FM stations. To find the factor by which one wavelength is larger than another, one can use the ratio of their frequencies.
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Related Practice
Textbook Question

Suppose you have a car with a 100-hp engine. How large a solar panel would you need to replace the engine with solar power? Assume that the solar panels can utilize 20% of the maximum solar energy that reaches the Earth’s surface (1000 W/m²). Explain why or why not this is practical.

Textbook Question

Who will hear the voice of a singer first: a person in the balcony 50.0 km away from the stage (see Fig. 31–26), or a person 1800 km away at home whose ear is next to the radio listening to a live broadcast? Roughly how much sooner? Assume the microphone is a few centimeters from the singer and the temperature is 20℃.


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Textbook Question

A satellite beams microwave radiation with a power of 16 kW toward the Earth’s surface, 550 km away. When the beam strikes Earth, its circular diameter is about 1500 m. Find the rms electric field strength of the beam.

Textbook Question

(III) (a) When a circular parallel-plate capacitor is being charged as in Example 31–1, show that the Poynting vector S→\(\overrightarrow{S}\) points radially inward toward the center of the capacitor, parallel to the plates.

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Textbook Question

(II) Laser light can be focused (at best) to a spot with a radius r equal to its wavelength ⋋. Suppose a 1.0-W beam of green laser light (⋋ = 5 x 10-7 m) forms such a spot and illuminates a cylindrical object of radius r and length r (Fig. 31–25). Estimate (a) the radiation pressure and force on the object, and (b) its acceleration, if its density equals that of water and it absorbs all the radiation. [This order-of-magnitude calculation convinced researchers of the feasibility of “optical tweezers,” page 916.]

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Textbook Question

An amateur radio operator wishes to build a receiver that can tune a range from 14.0 MHz to 15.0 MHz. A variable capacitor has a minimum capacitance of 95 pF.

(a) What is the required value of the inductance?

(b) What is the maximum capacitance used on the variable capacitor?

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