Electromagnetic waves
The idea
Light is a traveling disturbance in electric and magnetic fields: a changing electric field generates a changing magnetic field, which regenerates the electric field, and the pair propagates as an electromagnetic wave. Unlike sound, EM waves need no medium and cross empty space at c = 3.00 × 10⁸ m/s, the speed of light in vacuum. The familiar wave relation still rules: c = fλ, so frequency and wavelength are locked in an inverse trade.
The electromagnetic spectrum is one continuous family ordered by frequency: radio waves, microwaves, infrared, visible light (roughly 400 to 700 nm), ultraviolet, X-rays, and gamma rays. Radio wavelengths span meters; gamma wavelengths are smaller than atomic nuclei. Higher frequency means more energy carried per photon, which is why ultraviolet burns skin while radio waves pass through you unnoticed. Visible light is just the thin slice your eyes happen to detect.
The misconception to drop is that radio waves are sound waves. Radio is light your eyes cannot see — transverse, medium-free, moving at c — while sound is a longitudinal pressure wave in matter, about a million times slower in air. A radio receiver converts the EM signal into electrical oscillations and only then into the pressure waves your ears hear.
Worked example
An FM station broadcasts at 99.5 MHz. Find the wavelength of its radio waves, then find the frequency of green light with a wavelength of 550 nm, and compare the two waves. Use c = 3.00 × 10⁸ m/s.
- Both signals are electromagnetic waves, so each obeys c = fλ with the same speed c — only f and λ differ between them.
- For the radio wave, convert the frequency first: 99.5 MHz = 9.95 × 10⁷ Hz.
- Solve for its wavelength: λ = c/f = 3.00 × 10⁸ / 9.95 × 10⁷ ≈ 3.02 m — about the length of a small car, which is why FM antennas are meter-scale.
- For green light, convert the wavelength: 550 nm = 5.50 × 10⁻⁷ m, then f = c/λ = 3.00 × 10⁸ / 5.50 × 10⁻⁷ ≈ 5.45 × 10¹⁴ Hz.
- Compare the two: the light's frequency is millions of times the radio wave's and its wavelength is correspondingly millions of times shorter — yet both race through space at the same 3.00 × 10⁸ m/s.
Answer. The FM signal has a wavelength of about 3.02 m, while 550 nm green light oscillates at about 5.45 × 10¹⁴ Hz; both travel at c.
Check your understanding
- Why can electromagnetic waves cross the vacuum of space while sound waves cannot?
- How does knowing only the frequency of an EM wave let you place it on the spectrum and predict how it interacts with matter?
- What stays the same and what changes as you scan from radio waves up to gamma rays?
- Why do antennas for different services come in such different sizes, from rooftop dishes to the tiny antenna in a phone?
Build the foundations first
Electromagnetic waves builds on these concepts. If any feel shaky, start there.