Wavelength × frequency = wave speed: λ × f = v. The Toolenza calculator converts between any two given the third. Default is the speed of light (c = 299,792,458 m/s), but you can swap in sound (343 m/s in air), water waves, or any custom propagation speed.

The bands that matter

• Audible sound — 20 Hz to 20 kHz → wavelengths from 17 m down to 17 mm in air.
• AM radio — 530 to 1,700 kHz → wavelengths 175 to 570 m. Long enough to wrap around buildings; why AM works in tunnels FM doesn't.
• FM radio — 88 to 108 MHz → wavelengths about 3 m. Antennas are quarter-wave (75 cm), why car FM antennas are that size.
• WiFi — 2.4 GHz → 12.5 cm. 5 GHz → 6 cm. Why 5 GHz needs more access points for the same coverage.
• Visible light — 400 to 700 nm. Wavelength is the colour.
• X-rays — 0.01 to 10 nm. Wavelength is small enough to penetrate matter.

Pitfalls

Speed depends on medium. Sound in air is 343 m/s; in water 1,480 m/s; in steel 5,000 m/s. Light slows in glass (~200,000 km/s) and water (~225,000 km/s). Always check what medium the problem assumes — a single-frequency wave changes wavelength when it crosses media because the speed changes but the frequency does not.