Physics formulas

Oscillations, waves and sound

Calculate frequency, period, wavelength, and wave speed for periodic oscillations, sound, and other waves.

Formulas and calculators

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

T = 1 / f; v = λ × f

Calculated quantities

f - frequency · T - period · λ - wavelength · v - wave speed

T = 1 / f; v = λ × f

When to use it: The period is the reciprocal of the frequency, and a wave travels one wavelength during one period, so its speed equals wavelength times frequency.
Calculated quantities: f - frequency (Hz) · T - period (s) · λ - wavelength (m) · v - wave speed (m/s)
Worked example: Period of a 500 Hz tone: A tuning generator produces a tone of 500 Hz. Calculate the period of one oscillation and give it in milliseconds.

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.