Wave Speed Calculator

How to use this calculator

Enter any two of wave speed, frequency and wavelength — or use the period in place of the frequency. The angular frequency ω is shown as well, for use in wave equations of the form y = A sin(kx − ωt).

Wave speed is set by the medium, not the source. Typical values: sound 343 m/s in air at 20 °C, 1,481 m/s in fresh water, about 5,100 m/s in steel; light 299,792,458 m/s in vacuum and roughly 2.25 × 10⁸ m/s in water. For radio, enter the frequency in MHz with the speed of light to find antenna lengths.

The formula

v = f λ

T = 1 / f

ω = 2π f

v: wave speed
f: frequency
λ: wavelength
T: period
ω: angular frequency

Worked example

Concert A is 440 Hz. Sound travels at about 343 m/s in air at 20 °C. What is its wavelength?

λ = v / f = 343 / 440 = 0.780 m.
Period T = 1 / f = 2.27 ms.
Angular frequency ω = 2πf = 2,765 rad/s.

A 440 Hz tone has a wavelength of 78 cm in room-temperature air.

Speed of waves in common media

Wave and medium	Speed
Sound, dry air at 0 °C	331 m/s
Sound, dry air at 20 °C	343 m/s
Sound, fresh water at 20 °C	1,481 m/s
Sound (longitudinal), steel	≈ 5,900 m/s
Light / radio, vacuum	299,792,458 m/s (exact)

Assumptions and limits

A single, steady (monochromatic) wave in a uniform medium.
Speed depends on the medium and, for sound, on temperature: in air it rises about 0.6 m/s per °C.

Frequently asked questions

Does frequency change when a wave enters a new medium?

No — frequency is set by the source. The speed changes, so the wavelength changes in proportion.

What is the wavelength of FM radio?

At 100 MHz, λ = 299,792,458 / 100,000,000 ≈ 3.0 m, so a quarter-wave antenna is about 75 cm.

How do I convert wavelength to frequency for light?

Enter the speed of light, 299,792,458 m/s, and the wavelength in nm. Green light at 532 nm has a frequency of about 563 THz.

Wave Speed Calculator (v = fλ)