Wavelength and frequency calculator
Relates wave speed, frequency and wavelength in any direction.
Fill in the fields and the result will appear here automatically.
For a periodic wave, phase speed, frequency and wavelength satisfy v=fλ. Choose the unknown and enter the two known quantities; the third field is hidden and its previous value is ignored. Units are fixed: m/s, Hz and m, with period in seconds. Use the speed for the relevant wave, medium and frequency; there is no universal speed for every wave.
How it works
Formula and logic
The phase-speed relation is v=fλ; λ=v/f, f=v/λ and T=1/f. All known quantities must be positive. A wave packet’s group speed can differ from phase speed and is not calculated here.
Example
At 343 m/s in air, a 440 Hz note has a wavelength of 0.7795 m and a period of 0.002273 s.
Fields and units
- What to find — list option
- Wave speed — m/s
- Frequency — Hz
- Wavelength — m
How to use
- — Choose which of the three quantities you are looking for. Enter the two you already know. Use the speed of the medium, not of the source. The period T=1/f is the time of one complete cycle, in seconds.
- — Check unit conversion:1 kHz=1000 Hz and 1 cm=0.01 m. For example,50 Hz gives T=0.02 s regardless of λ.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax §16.1: speed, wavelength, frequency and period OpenStax §6.5: λ=h/p, limits of p=mv and matter-wave frequency
- Limitation
- The phase-speed relation is v=fλ; λ=v/f, f=v/λ and T=1/f. A wave packet’s group speed can differ from phase speed and is not calculated here.
FAQ
What wave speed should I use?
The speed in the medium the wave travels through: roughly 343 m/s for sound in air at room temperature, about 1,500 in water, and 299,792,458 for light in vacuum.
Does higher frequency always mean unchanged speed?
In a nondispersive model the speed is unchanged and greater frequency shortens λ. In a dispersive medium, phase speed depends on frequency, so use the speed at that frequency. Across a stationary boundary the frequency remains unchanged while wavelength follows the phase speed.
What is the difference between frequency and period?
They are reciprocals of one another. Fifty hertz is a period of 0.02 seconds; the first counts cycles per second, the second measures one cycle.
Does this work for light and radio?
Yes, with the appropriate speed. In vacuum use 299,792,458 m/s; inside glass or cable the speed is lower and the wavelength shortens accordingly.