Oscillations, waves and sound

Wave frequency, period and speed

Calculate the frequency, period, wavelength, or speed of a wave from two related equations: T = 1 / f and v = λ × f.

Formula

T = \frac{1}{f}; v = λ f

The period is the reciprocal of the frequency, and a wave travels one wavelength during one period, so its speed equals wavelength times frequency.

Wave frequency, period and speed calculator

Symbol	Quantity	SI	Supported units
f	frequencyNumber of full oscillations per second. One hertz is one cycle per second, that is 1 Hz = 1 s⁻¹.	Hz	Hz, kHz, MHz, GHz
T	periodTime of a single full oscillation, not the duration of the whole signal.	s	s, ms, µs
λ	wavelengthDistance between two neighbouring points of the wave in the same phase, for example two crests.	m	m, cm, mm, km
v	wave speedSpeed at which the phase of the wave travels through the medium; it depends on the medium, not on how hard the source is driven.	m/s	m/s, km/h

Period from frequency

T = 1 / f

Frequency from period

f = 1 / T

Speed from wavelength and frequency

v = λ × f

Speed from wavelength and period

v = λ / T

Wavelength from speed and frequency

λ = v / f

Wavelength from speed and period

λ = v × T

Frequency from speed and wavelength

f = v / λ

Period from speed and wavelength

T = λ / v

A tuning generator produces a tone of 500 Hz. Calculate the period of one oscillation and give it in milliseconds.

Result: 2 ms (0.002 s)

Sound travels through air at about 340 m/s. Calculate the wavelength of a 680 Hz tone in that air.

1Step 1: Rearrange v = λ × f into λ = v / f.
2Step 2: Substitute v = 340 m/s and f = 680 Hz.
3Step 3: Calculate λ = 340 / 680 m = 0.5 m.
4Step 4: Check the units: (m/s) / s⁻¹ gives metres, so the result is a length, not a time.

Result: 0.5 m (50 cm)

13.2 Wave Properties: Speed, Amplitude, Frequency, and Period
OpenStax · Reviewed 29 August 2026
Definitions of period, frequency, wavelength, and the relationships T = 1 / f and v = λ f.
13.1 Types of Waves
OpenStax · Reviewed 29 August 2026
Scope of the model: periodic transverse and longitudinal waves travelling through a medium.
SI Brochure: The International System of Units (SI), 9th edition
Bureau International des Poids et Mesures · Reviewed 29 August 2026
Definition of the hertz as the SI unit of periodic frequency, equal to s⁻¹, and the rules for SI prefixes.

The wave is periodic and travels through a uniform medium, so its speed stays constant along the considered path.
The wave speed is set by the medium; changing the frequency changes the wavelength, not the speed.
Frequency, period, wavelength, and wave speed are all greater than zero, so none of them may be entered as zero or a negative number.
Frequency f in hertz counts full cycles per second and must not be confused with angular frequency ω = 2πf, which is given in rad/s.
The period T is the time of one oscillation, not the duration of the whole signal or measurement.

Confusing frequency f in hertz with angular frequency ω in rad/s and dropping the factor 2π.
Treating the period as the duration of the whole signal instead of the time of a single oscillation.
Mixing prefixes, for example dividing metres by megahertz without converting MHz to hertz first.
Assuming that a higher frequency means a higher wave speed; in a given medium it means a shorter wavelength.
Reporting a wavelength in seconds, which happens when λ = v / f is used with the operands swapped.