Wave speed
Propagation phase speed of the periodic wave.
Physics · Mechanics · Motion & Energy
Wave speed, frequency and wavelength calculator
Find wave speed, frequency, wavelength or period from v = fλ. This is the propagation speed of a periodic wave, not the velocity of the medium’s particles.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Frequency
Number of complete cycles per second.
Wavelength
Spatial distance between successive wave crests.
Period
Duration of one complete cycle.
Relation and numerical substitution
v = f × λ—
Periodic travelling wave; positive speed, frequency and wavelength.
01Formulas and symbols
Formulas used
v
v = f × λPropagation phase speed of the periodic wave.f
f = v / λNumber of complete cycles per second.λ
λ = v / fSpatial distance between successive wave crests.T
T = 1 / fDuration of one complete cycle.02Assumptions and limits
Scope of validity
- Periodic travelling wave; positive speed, frequency and wavelength.
03Validation example
Reference numerical case
- f = 50 Hz and λ = 2 m: v = 50 × 2 = 100 m/s and T = 1/50 = 0.02 s. Inverse modes recover f = 50 Hz or λ = 2 m.
04References
Technical references
FAQ
Does increasing frequency always increase wave speed?
No. In a non-dispersive medium the propagation speed is set mainly by the medium, so changing frequency changes wavelength instead. In a dispersive medium, phase speed can itself depend on frequency.
How are frequency and wavelength related when wave speed is fixed?
From v = fλ, wavelength is λ = v/f. At fixed wave speed, doubling the frequency halves the wavelength.
05How it works
In one period the wave travels one wavelength, so v = λ/T = fλ. At a fixed propagation speed, doubling frequency halves wavelength. The period mode takes speed and wavelength and also returns the corresponding frequency.
06Limits of the model
Positive quantities for a periodic travelling wave. In a dispersive medium, use phase speed at the frequency of interest; the relation does not determine group velocity. This calculator does not predict speed from tension, density or temperature.
07Common mistakes
Wavelength is the distance between two successive crests, not crest to trough. Convert kHz to Hz through the selector. Increasing source frequency does not automatically increase propagation speed in a nondispersive medium.