〰️ Wave Speed Calculator
v = f × λ. Solve for wave speed, frequency, or wavelength.
Result
How to Use This Calculator
Choose whether to solve for wave speed (m/s), frequency (Hz), or wavelength (m), then enter the two known values. The equation applies to any type of wave: sound in air, sound in water, light, radio waves, or waves on a string.
Select the variable to solve for: Wave Speed, Frequency, or Wavelength from the dropdown.
Enter frequency in hertz (Hz). For audio, middle A = 440 Hz. For FM radio, a typical station is around 100 MHz = 100,000,000 Hz.
Enter wavelength in metres. For sound in air, a 440 Hz note has wavelength λ = 343 / 440 = 0.78 m.
Enter wave speed in m/s when solving for frequency or wavelength. Use 343 for sound in air at 20°C, or 3×10⁸ for light in a vacuum.
Wave Speed Formula
For a fixed wave speed in a given medium, frequency and wavelength are inversely proportional. Double the frequency and the wavelength halves. This is why bass notes (low frequency) have long wavelengths and treble notes (high frequency) have short ones. The speed itself changes when the wave moves to a different medium, but the frequency stays the same.
Worked Examples
Where This Comes Up in Real Life
Sonar systems on ships and submarines measure water depth by sending a sound pulse and timing the echo. With sound traveling at 1480 m/s in seawater, a return echo after 0.2 seconds means the pulse traveled 1480 × 0.2 = 296 m round-trip, so the depth is 148 m. The frequency of the pulse also matters: higher frequencies give better resolution but do not travel as far because they are absorbed more quickly.
Mobile phone networks transmit in frequency bands between roughly 700 MHz and 3.5 GHz. At 1 GHz, the wavelength is λ = 3×10⁸ / 10⁹ = 0.3 m. This determines the size of the antennas: an efficient antenna needs to be about a quarter of a wavelength long, so 7.5 cm. 5G networks use 28 GHz frequencies, giving λ = 10.7 mm and antennas small enough to pack dozens into a phone.
Frequently Asked Questions
What is the wave equation?
v = f × λ, where v is wave speed (m/s), f is frequency (Hz), and λ (lambda) is wavelength (m).
What is the speed of sound?
In air at 20°C: ~343 m/s. In water: ~1480 m/s. In steel: ~5960 m/s.
What is the wavelength of middle C?
Middle C = 261.63 Hz. λ = v/f = 343/261.63 ≈ 1.31 m.
Is light speed always 3×10⁸ m/s?
The speed of light in vacuum c = 2.998×10⁸ m/s. In other media it is slower: v = c/n where n is the refractive index.
How are frequency and wavelength related?
They are inversely proportional at constant wave speed. Higher frequency = shorter wavelength.