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Chapter 14: Problem 18

An 88.7 -MHz FM radio wave propagates at the speed of light. What's its wavelength?

Short Answer

Expert verified
The wavelength of the 88.7-MHz FM radio wave is approximately 3.38 meters.

Step by step solution

01

Understand the Given Values

The frequency of the radio wave (\(f\)) is given as 88.7 MHz, which is equal to \(88.7 × 10^6\) Hz. The speed of a radio wave (\(v\)), like all electromagnetic waves in a vacuum, is the speed of light, \(3 × 10^8\) m/s.
02

Use the Wave Speed Formula

To find the wavelength (\(λ\)), the formula \(v = fλ\) can be rearranged to \(λ = v / f\). This calculates the wavelength of the wave.
03

Substitute the Given Values

Substitute the given values into the equation. This gives \(λ = (3 × 10^8) / (88.7 × 10^6)\). Solving this expression will yield the wavelength of the radio wave in meters.
04

Calculate the Wavelength

Solving the expression \(λ = (3 × 10^8) / (88.7 × 10^6)\) gives a wavelength (\(λ\)) of approximately 3.38 meters.

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Most popular questions from this chapter

When a wave source moves relative to the medium, a stationary observer measures changes in both wavelength and frequency. But when the observer moves and the source is stationary, only the frequency changes. Why the difference?

Light emerges from a 5.0 -mW laser in a beam 1.0 mm in diameter. The beam shines on a wall, producing a spot \(3.6 \mathrm{cm}\) in diameter. What is the beam's intensity (a) at the laser and (b) at the wall?

The intensity of light from a localized source decreases as the inverse square of the distance from the source. Does this mean that the light loses energy as it propagates?

Must a wave be either transverse or longitudinal? Explain.

A heavy cable is hanging vertically, its bottom end free. How will the speed of transverse waves near the top and bottom of the cable compare? Why?
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