Wavelength and frequency are linked by a simple rule: for a given wave speed, they are inversely proportional—when one goes up, the other must go down.

The core relationship

For any wave moving through a medium with speed vvv, the basic equation is:

v=fλv=f\lambda v=fλ

where:

  • vvv = wave speed (meters per second),
  • fff = frequency (Hertz, cycles per second),
  • λ\lambda λ = wavelength (meters).

If the speed vvv stays the same (same medium, same conditions), then:

  • Increasing frequency fff forces wavelength λ\lambda λ to decrease.
  • Increasing wavelength λ\lambda λ forces frequency fff to decrease.

That is what “inversely related” means.

Intuitive picture

Imagine you are standing on a pier watching water waves go by:

  • Short-wavelength waves (crests close together) mean more crests hit you each second → higher frequency.
  • Long-wavelength waves (crests far apart) mean fewer crests per second → lower frequency.

The water’s wave speed under the same conditions doesn’t change much, so packing crests closer together is the only way to increase how many pass each second.

Special case: light in a vacuum

For electromagnetic waves in vacuum, the speed is the constant speed of light ccc, so:

c=fλc=f\lambda c=fλ

  • High-frequency light (like violet or ultraviolet) has short wavelength.
  • Low-frequency light (like red or radio waves) has long wavelength.

Again, because ccc is fixed, fff and λ\lambda λ must trade off.

Mini example

Take visible red light:

  • Speed c≈3.0×108c\approx 3.0\times 10^8c≈3.0×108 m/s.
  • Wavelength λ≈7.0×10−7\lambda \approx 7.0\times 10^{-7}λ≈7.0×10−7 m.

Frequency is:

f=cλf=\dfrac{c}{\lambda}f=λc​

So if you doubled the wavelength (in a medium where speed stays the same), the frequency would be cut in half.

Information gathered from public forums or data available on the internet and portrayed here.