Frequency ↔ Wavelength ↔ Period
Converts between the frequency, period and wavelength of a periodic wave. Enter whichever one you know and the page gives the other two. Radio and RF engineers use it to cut antennas and coax stubs, acoustics engineers to find the wavelength of a tone in air or water, and NDT technicians to relate an ultrasonic frequency to its wavelength in steel.
Equations
T = 1/f v = f·λ
f is the frequency in hertz (cycles per second), T the period in seconds (the time for one cycle), λ the wavelength in meters (the distance the wave travels in one cycle) and v the propagation velocity in meters per second [1]. The period depends only on the frequency. The wavelength also depends on the medium, through v.
Inputs
- Known Unit picks which of frequency, period or wavelength you enter. Each field has its own unit picker.
- Wave & medium fills in a typical propagation velocity. Electromagnetic waves travel at c = 299,792,458 m/s in vacuum, and at c/n in a material of refractive index n, or VF × c in a cable of velocity factor VF. Sound travels at about 343 m/s in air at 20 °C, 1,481 m/s in fresh water and 5,960 m/s in steel.
- Propagation velocity (v) can be typed directly for any other medium, such as a cable whose datasheet gives a different velocity factor.
Limits and common mistakes
- The page assumes v is the same at every frequency. Real cables, optical fiber and water are slightly dispersive, so a preset is a good typical value, not an exact one.
- Leaving v at the vacuum value when the wave is in a cable or a solid. A stub cut to the free-space wavelength in coax with VF 0.66 comes out about 50 % too long.
- The speed of sound in air rises about 0.6 m/s for each °C, so pick the preset nearest the actual temperature or enter v yourself.
- A wire antenna is cut a few percent shorter than the free-space quarter or half wavelength, because of end effects. Use the page’s wavelength as the starting point, then trim.
Worked example
An open-ended quarter-wave stub is needed to notch a 145 MHz signal, made from RG-58 coax with a solid polyethylene dielectric. How long should the stub be?
- Choose Known Unit Frequency.
- Choose Wave & medium Coax, solid PE dielectric (VF 0.66). Propagation velocity (v) fills in as 197,863,022 m/s.
- Enter Frequency (f) 145 MHz.
- Press Solve. The Solution shows:
Period (T): 6.89655e-9 s
Wavelength (λ): 1.36457 m
The quarter wave is 1.36457 / 4 = 0.341 m, so cut the stub about 341 mm long, then trim it on an analyzer. Check by hand: the free-space wavelength is 300/145 = 2.07 m, and 0.66 × 2.07 = 1.36 m. The period is 1/(145 × 106) = 6.9 ns.