In the United States, the ac household current oscillates at...

In the United States, the ac household current oscillates at a frequency of $60 \mathrm{Hz}$. In the time it takes for the current to make one oscillation, how far has the electromagnetic wave traveled from the current-carrying wire? This distance is the wavelength of a $60 \mathrm{Hz}$ EM wave. Compare this length with the distance from Boston to Los Angeles $(4200 \mathrm{km})$.

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Key Concepts

Electromagnetic Wave Propagation

Electromagnetic waves, such as light or radio waves, travel through space at a constant speed in a vacuum—approximately 3 x 10^8 meters per second. This property is key in understanding how quickly the wave covers distance relative to its oscillation period.

Frequency-Wavelength Relationship

There is a fundamental relationship between the frequency, wavelength, and speed of an electromagnetic wave expressed as ? = c / f, where ? (wavelength) indicates the distance a wave travels during one complete cycle, c is the speed of light, and f is the frequency. This formula provides the method for calculating the wavelength when the frequency is known.

Scale Comparison

Comparing the calculated wavelength (which is determined by the low frequency of 60 Hz) with a large geographic distance involves understanding orders of magnitude. This comparison emphasizes how the relatively short wavelength of a low-frequency electromagnetic wave (typically much shorter than everyday distances like those between cities) stands in contrast with the vast scale of terrestrial distances.

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