Maxwell's equations, written down in 1865, predicted that the empty space of vacuum could carry electromagnetic waves propagating at exactly one specific speed: 1/√(μ₀·ε₀) ≈ 3 × 10⁸ m/s. The number agreed almost exactly with the measured speed of light. Maxwell wrote the consequence carefully: "*This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself … is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field.*" Within fifteen years, Heinrich Hertz (1887) had generated and detected radio waves in his lab — electromagnetic waves at frequencies far below visible light. The full electromagnetic spectrum — radio, microwave, infrared, visible, ultraviolet, X-ray, gamma — was, at one stroke, revealed as one phenomenon at different wavelengths.
The mechanism Maxwell's equations described is delicately self-sustaining. A changing electric field generates a magnetic field through the Ampère-Maxwell law; the changing magnetic field generates an electric field through Faraday's law; the two regenerate each other and propagate forward through space at the speed c = 1/√(μ₀ε₀). The fields oscillate perpendicular to each other and to the direction of motion, which is why electromagnetic waves are transverse, and the wavelength and frequency are tied by c = λν. What makes the picture remarkable is the range of phenomena it unifies. Radio, microwave, infrared, visible light, ultraviolet, X-ray, and gamma rays span more than fifteen orders of magnitude in wavelength and look, on the surface, nothing alike — radio waves pass through walls, microwaves heat water, infrared is felt as warmth, visible light forms images in the eye, X-rays penetrate flesh, gamma rays ionize everything in their path — but they are the same phenomenon at different scales, and Hertz's 1887 detection of radio waves in his lab settled the unification.
What the wavelength governs is how the wave couples to matter, and the coupling determines almost everything practical about the spectrum. Photon energy E = hν scales with frequency, so the same electromagnetic field is a gentle warming infrared photon at one wavelength and a DNA-damaging ultraviolet photon at another. Molecules, atoms, and electronic transitions each have characteristic energy gaps that match particular bands, which is why visible light is the band our eyes detect (the gap matches retinal pigments), why microwaves heat water (the gap matches a rotational mode of H₂O), and why X-ray crystallography works (the wavelength matches inter-atomic distances). The classical optical phenomena — diffraction, interference, refraction, polarization, Doppler shift — all follow directly from applying Maxwell's equations to waves, and the cosmological redshift from cosmic expansion is the same mechanism evaluated over enormous distances. One set of equations governs everything from the warmth of sunlight to the detection of gravitational lensing.
Wireless communication of every kind — broadcast radio, cellular telephony, Wi-Fi, 5G, satellite internet — is engineered control over the generation, propagation, and reception of electromagnetic waves at carefully chosen wavelengths. Optical fiber sends data through dielectric waveguides at infrared wavelengths; radar and lidar image with reflected waves; astronomy now observes the universe across the entire spectrum, from the ALMA millimeter array and JWST infrared telescope through Hubble's visible to Chandra's X-rays and Fermi's gamma-ray observations. X-ray crystallography and free-electron lasers image atomic and molecular structure, photovoltaic panels convert sunlight into electricity, and gravitational lensing has become a routine cosmological tool. The Maxwell prediction of 1865 is, by any reasonable accounting, the technological cornerstone of modern civilization.