Wave Speed Calculator

Wave speed equals frequency times wavelength: v = f × λ. Provide frequency in hertz and wavelength in metres, and you get speed in m/s. So a sound wave at 1000 Hz with wavelength 0.343 m travels at 343 m/s — exactly the speed of sound at room temperature. Light at 500 nm has frequency 6×10^14 Hz, giving v = 3×10^8 m/s, the speed of light. This relationship works for every kind of wave — sound, light, water, seismic. Calculators just run the multiplication. The formula's universality is one of the most elegant things in physics.

Multiply: v = fλ. With frequency in hertz and wavelength in metres, speed comes out in m/s. So a 50 Hz sound wave with wavelength 6.86 m travels at 343 m/s — speed of sound at 20 °C in air. A radio wave at 100 MHz with 3 m wavelength travels at 3×10^8 m/s — the speed of light. The same equation governs every wave type: the medium dictates speed, and within a medium, frequency and wavelength trade off inversely so their product stays constant. Pretty remarkable when you think about it — one formula across acoustics, optics, and seismology.

Rearrange v = fλ to f = v/λ. With v in m/s and λ in metres, frequency comes out in hertz. So sound (v = 343 m/s) with 0.5 m wavelength gives f = 686 Hz, near a musical F5. Light at 600 nm (6×10^-7 m) has f = 5×10^14 Hz. This is the form to use when you've measured wavelength directly (say with a ruler on a string wave or a spectroscope on light) and want to know the frequency. Useful in astronomy, where redshifted wavelengths reveal source frequencies and recession velocities of distant galaxies.

Rearrange v = fλ to λ = v/f. So a 440 Hz tone in air (v = 343 m/s) has λ = 343/440 ≈ 0.78 m — about a sound-pipe length for that pitch. A 5 GHz Wi-Fi signal in vacuum has λ = 3×10^8/5×10 = 0.06 m, or 6 cm — which is why your router's antenna isn't very long. The calculator manages units automatically. This formula is essential for antenna design, musical instrument acoustics, and any application where physical size has to match a wave property — like sound chambers, microwave ovens, or radio horns.

v = fλ — three letters, one equation, governs every wave. Wave speed v depends on the medium (air at 343 m/s, water at 1480 m/s, vacuum for light at 3×10^8 m/s). Frequency f and wavelength λ adapt to maintain that constant product within a given medium. Higher frequency, shorter wavelength, and vice versa. Crossing into a new medium changes v but keeps f the same — the wave doesn't suddenly oscillate at a different rate. So when light enters water and slows down, its wavelength shrinks correspondingly. Memorise v = fλ; you'll use it more than almost any other physics formula.

Sound in air at 20 °C travels at v ≈ 343 m/s. So a 1 kHz tone has λ = 0.343 m; a 100 Hz bass tone has λ = 3.43 m. Sound speed varies with temperature (faster in warm air), humidity (slightly faster in moist air), and medium (much faster in water and solids). For a 20 kHz human-hearing-limit ultrasonic, λ in air is only 17 mm. Music ranges roughly 20 Hz to 20 kHz, so wavelengths span 17 mm to 17 m — quite a range, which explains why bass speakers need to be large to reproduce low notes faithfully.

Most calculators support Hz and metres natively, but accept kHz, MHz, GHz on the frequency side and mm, cm, µm, nm on the wavelength side. The relationship v = fλ stays the same regardless of unit prefixes — internally the calculator converts to base SI. So a 2.4 GHz Wi-Fi signal corresponds to λ = 12.5 cm in vacuum. A 500 nm green photon has frequency 6×10^14 Hz. Specifying units explicitly avoids the all-too-common error of forgetting that GHz means 10 Hz or µm means 10^-6 m. Take your time with the prefixes, and the answer drops out cleanly.