Radio waves have _______ wavelength and _________ frequency relative to visible light

Question

BlackTom AI · Accepted Answer

c = λ·f for electromagnetic waves in vacuum, and c (speed of light) is essentially constant (~3.00 × 10^8 m/s). That means wavelength (λ) and frequency (f) are inversely related: if one increases, the other decreases.

1) Relevant knowledge points and concepts
- All electromagnetic waves travel at the same speed in vacuum: c ≈ 3.00 × 10^8 m/s.
- Relationship: c = λ · f. Thus λ ∝ 1/f (longer wavelength → lower frequency).
- Typical orders of magnitude: visible light wavelengths ≈ 400–700 nm (4.00×10^-7 to 7.00×10^-7 m). Visible frequencies ≈ c/λ → about 4.3×10^14 to 7.5×10^14 Hz. Radio wavelengths range from millimeters to kilometers and radio frequencies from about 3×10^4 Hz up to ~3×10^11 Hz, typically much lower than visible frequencies.

2) Step-by-step reasoning
- Use c = λ·f and compare representative values.
- Example radio frequency: 100 MHz = 1.00×10^8 Hz.
- Compute corresponding radio wavelength: λ = c / f = (3.00×10^8 m/s) / (1.00×10^8 s^-1) = 3.00 m.
- Compare to visible wavelength (take 600 nm = 6.00×10^-7 m): 3.00 m is vastly larger than 6.00×10^-7 m, so radio waves have a longer wavelength.

3) Calculations (intermediate steps shown)
- Radio example: f_radio = 1.00×10^8 Hz
- λ_radio = c / f_radio = (3.00×10^8 m/s) / (1.00×10^8 s^-1) = 3.00 m
- Visible example: λ_vis ≈ 6.00×10^-7 m → f_vis = c / λ_vis = (3.00×10^8) / (6.00×10^-7) ≈ 5.00×10^14 Hz
- Compare frequencies: 1.00×10^8 Hz (radio) << 5.00×10^14 Hz (visible) → radio frequency is much smaller.

4) Why the correct answer is correct
Because for the same wave speed, radio waves occupy much longer wavelengths than visible light; by the inverse relation, that longer wavelength corresponds to a much smaller frequency.

5) Why the other options are incorrect
- a (longer, larger): contradicts c = λ·f (longer wavelength implies smaller frequency, not larger).
- b (shorter, smaller): radio wavelengths are not shorter than visible; they are longer.
- c (shorter, larger): both parts are opposite of reality.

Conclusion: Radio waves have longer wavelength and smaller frequency relative to visible light, so option d (longer, smaller) is correct.

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Radio waves have _______ wavelength and _________ frequency relative to visible light单项选择题

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Radiation needs a medium to travel.

Radiation needs a medium to travel.

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He showed that light is an electromagnetic wave.

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希望你的学习变得更简单

Radio waves have _ wavelength and ___ frequency relative to visible light单项选择题