Wavelength and Frequency
Wavelength and frequency are inversely related properties of any wave. For electromagnetic waves, they are connected through the speed of light. For sound waves, they connect through the speed of sound in the medium. As frequency increases, wavelength decreases proportionally, and vice versa.
This relationship is fundamental to radio engineering, optics, acoustics, and quantum mechanics. Converting between wavelength and frequency allows scientists to describe the same wave property using whichever unit is most convenient for their application.
The Formula
Where f is frequency (Hz), v is wave speed (m/s), and λ is wavelength (m). The period T = 1/f gives the time for one complete oscillation cycle.
EM Spectrum Reference
| Type | Wavelength | Frequency |
|---|---|---|
| AM Radio | 100-1000 m | 300 kHz - 3 MHz |
| FM Radio | 3-4 m | 88-108 MHz |
| WiFi (2.4 GHz) | 12.5 cm | 2.4 GHz |
| Visible (green) | 550 nm | 545 THz |
| X-rays | 0.01-10 nm | 30 PHz - 30 EHz |
Frequently Asked Questions
Does frequency change when light enters glass?
No. When light enters a denser medium like glass, frequency stays the same but wavelength decreases because the speed of light is slower in the medium. The relationship v = fλ still holds, but v is now smaller than c.
What is the frequency of visible light?
Visible light spans approximately 430 THz (red, 700 nm) to 790 THz (violet, 380 nm). The peak sensitivity of the human eye is at about 555 nm (540 THz), corresponding to yellow-green light.
How do I convert frequency to wavelength for sound?
Use the same formula with the speed of sound instead of light. In air at 20 degrees C, v = 343 m/s. So a 440 Hz note (concert A) has a wavelength of 343/440 = 0.78 meters.