The wavelength and frequency of a wave are inversely related: as frequency increases, wavelength decreases, and vice versa, for a wave traveling at a fixed speed in a given medium. The fundamental relationship is: v = f λ where:
- v is the wave speed in the medium (meters per second),
- f is the frequency (cycles per second or Hz),
- λ is the wavelength (meters).
Key points:
- In a given medium, v is determined by the medium’s properties (e.g., air, water, vacuum for light), so changing f changes λ to keep the product f λ equal to v.
- If the medium is constant and the frequency doubles, the wavelength halves.
- For electromagnetic waves in a vacuum, v equals the speed of light c (approximately 3.00 × 10^8 m/s), so λ = c / f.
- The inverse relationship holds for all wave types (sound, light, water waves) as long as the wave speed in the medium is fixed during the comparison.
Examples:
- Sound in air at room temperature travels about 343 m/s. If the sound has a frequency of 686 Hz, its wavelength is λ = v / f ≈ 343 / 686 ≈ 0.5 m. Doubling the frequency to 1372 Hz would yield λ ≈ 0.25 m.
- Light in a vacuum with f = 6.0 × 10^14 Hz (roughly a green photon) has λ = c / f ≈ 5.0 × 10^-7 m (500 nm). A higher frequency (shorter wavelength) corresponds to a higher-energy photon.
