====== Frequency and wavelength ======

**Frequency** is the number of cycles per second, measured in hertz (Hz). **Wavelength** is the distance occupied by one cycle of a travelling wave. Their relationship helps explain band names, antenna dimensions and electrical lengths.

===== Basic relationship =====

<code>
λ = v / f
λ ≈ 300 / f_MHz          (metres, free-space estimate)
</code>

λ is wavelength in metres, v is propagation speed in metres per second and f is frequency in hertz. In vacuum, v equals the speed of light, 299,792,458 m/s. Air is close enough to vacuum for many initial antenna estimates.

^ Frequency ^ Approximate free-space wavelength ^ Quarter wavelength ^
| 7 MHz | 42.8 m | 10.7 m |
| 14 MHz | 21.4 m | 5.35 m |
| 27 MHz | 11.1 m | 2.78 m |
| 144 MHz | 2.08 m | 0.520 m |

The [[citizens_band_radio|27 MHz CB band]] is called 11 metres because of its approximate wavelength. A band name is a convenient label; it is not an exact wavelength at every frequency in that band.

===== Electrical length =====

An [[antenna|antenna]] with a quarter-wave electrical length is not necessarily a wire exactly one quarter of a free-space wavelength long. Geometry, conductor thickness, insulation, loading and nearby objects affect its behaviour.

Waves also travel more slowly in a [[transmission_line|transmission line]] than in free space. With a cable velocity factor VF:

<code>
Cable wavelength = VF c / f
</code>

At 27 MHz, a cable with VF = 0.66 has a wavelength of about 7.33 m. Its quarter-wave electrical length is therefore about 1.83 m. This is a cable example, not a prescription for the length of a radiating antenna.

===== References =====

  * [[https://openstax.org/books/physics/pages/15-2-the-behavior-of-electromagnetic-radiation|OpenStax: frequency and wavelength]].
  * [[https://openstax.org/books/university-physics-volume-2/pages/16-2-plane-electromagnetic-waves|OpenStax: electromagnetic wave propagation]].