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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: 9780137488179당신이 사용하는 게 아니라요?교과서 변경
30장, 문제 42

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

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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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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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