Waves and Frequency

The idea

Throw a stone into a calm pond and ripples spread outward in circles. A radio wave is the same idea, except the ripple is in electric and magnetic fields instead of water — and it needs no pond at all. It travels through air, walls, and the vacuum of space, always at the speed of light: about 300,000 kilometers per second, fast enough to circle the Earth 7.5 times in one second.

Radio waves are everywhere. Your phone talks to a cell tower kilometers away, WiFi carries web pages from your router, a key fob unlocks your car across a parking lot, and GPS satellites beam signals down from 20,000 km up. It is all the same physical thing — an electromagnetic wave — used at different frequencies. In fact, radio waves and visible light are the same phenomenon; the only difference is how fast they wiggle. Your eyes detect one narrow slice of the electromagnetic spectrum; a radio detects another.

Two numbers describe every radio wave. Frequency (f) counts how many times the wave wiggles per second, in hertz (Hz): AM radio wiggles about 1 million times per second (1 MHz), FM radio about 100 million (100 MHz), and WiFi about 2.4 billion (2.4 GHz). Wavelength (λ, "lambda") is the physical distance from one wave peak to the next, in meters.

The math

All radio waves travel at the same speed, so speed equals wiggles per second times length per wiggle:

$$c = f \lambda$$

where c is the speed of light (about 3×10⁸ m/s), f is frequency in Hz, and λ is wavelength in meters. Because c never changes, frequency and wavelength sit on a see-saw: when one goes up, the other must come down.

A handy mental shortcut: wavelength in meters equals 300 divided by frequency in MHz.

$$\lambda \text{ (m)} \approx \frac{300}{f \text{ (MHz)}}$$

So 100 MHz FM radio has a 3 m wavelength, 2.4 GHz WiFi has a 12.5 cm wavelength, and 1 MHz AM radio has a 300 m wavelength. This is why an AM broadcast tower is a 100-meter steel giant while the WiFi antenna in your phone is a copper squiggle a few centimeters long — antennas work best when their size matches the wavelength.

Common misconceptions

• Myth: Radio waves are vibrations of air, like sound. Reality: They are ripples in electric and magnetic fields and need no medium at all — they cross the vacuum of space, which sound cannot.
• Myth: Higher-frequency waves travel faster. Reality: All electromagnetic waves travel at the same speed of light. Higher frequency only means shorter wavelength.
• Myth: Radio and light are fundamentally different things. Reality: They are the same electromagnetic phenomenon at different frequencies — a radio is essentially an eye tuned to a different slice of the spectrum.

Try it

Open the EM Fundamentals lab and drag the frequency slider: watch the wave squeeze together as frequency rises and stretch out as it falls — that is c = fλ happening live. Try to find the frequency where the wavelength is exactly 1 meter.