Wavelength and frequency converter
A 40 Hz tone has a wavelength of 8.6 metres in air. In a room four metres across, that wave cannot complete a cycle before hitting a wall, which is why low frequencies produce standing waves, room modes and the familiar problem of bass that is deafening in one corner and absent in another. Room treatment for bass has to be physically large for exactly this reason, because the wavelengths are.
Wave speed divided by wavelength gives frequency; divided by frequency it gives wavelength. Sound travels about 343 m/s in dry air at 20 °C, so a one-metre wave is 343 Hz and concert A at 440 Hz measures 0.78 m. In water at 1,481 m/s the same wave is four times longer.
How to convert between wavelength and frequency
The speed of sound in air varies with temperature, rising roughly 0.6 m/s for every degree Celsius. At 0 °C it is 331 m/s and at 30 °C about 349. A 5% spread that matters for precise acoustic work and not at all for a rough figure. Humidity has a much smaller effect, and pressure essentially none, which surprises people who expect altitude to change it. What altitude actually changes is temperature.
The range is the whole story
Audible wavelengths span a factor of a thousand: over seventeen metres at 20 Hz down to seventeen millimetres at 20 kHz. That single fact explains most of what is awkward about acoustics. High frequencies are directional and easily absorbed because they are small compared with the objects in a room, so a tweeter needs aiming and a curtain kills the top end. Low frequencies wrap around obstacles and interact with the room dimensions themselves, which is why bass leaks through walls, why a small speaker cannot produce it efficiently, and why the same note is deafening in one corner and absent in another.
A quarter of it is the number you actually use
The quarter wavelength is the figure that gets used in practice. A porous absorber works best at about a quarter of the wavelength deep, so treating 100 Hz properly asks for something close to 86 cm, so serious bass traps end up as furniture and not panels. A quarter-wave antenna follows the same arithmetic in the vacuum column: at 300 MHz the wavelength is one metre, so the antenna is 25 cm.
Two speeds, and picking the wrong one is a factor of a million
Sound and light share the formula and nothing else. Air carries sound at roughly 343 m/s; electromagnetic waves travel at 299,792,458 m/s in a vacuum, and a little slower in cable or glass. Feeding an acoustic frequency into the light figure, or the reverse, does not produce a slightly wrong answer — it produces one about 874,000 times out, which at least announces itself. The subtler version is the one that bites: a wave in coaxial cable moves at the velocity factor of its dielectric, typically 0.66 to 0.85 of the vacuum speed, so a quarter-wave stub cut from the vacuum wavelength is around half as long again as it should be. Put the cable’s actual speed in the custom field rather than trimming afterwards.
What people use it for
- Room acoustics and standing waves
- Sizing acoustic absorption from the quarter wavelength
- Antenna and speaker design
- Working out speaker placement
- Understanding why bass traps are large
- Physics homework
Questions
f = v ÷ λ in one direction and λ = v ÷ f in the other. Both are wave speed divided by the figure you already have.
About 0.78 metres in air at 20 °C. Concert A is roughly the length of a forearm.
Over seventeen metres, longer than most rooms, which is why deep bass is so hard to control indoors.
About 343 m/s in dry air at 20 °C, rising roughly 0.6 m/s per degree.
Porous absorbers work best at about a quarter of the wavelength deep, so treating low frequencies needs physically deep panels, not thin ones.
Enormously. Sound travels more than four times faster in water, so a wave at the same frequency is more than four times longer.
Only through temperature. Pressure itself has essentially no effect.
Choose the vacuum option. Light travels at 299,792,458 m/s, so a one-metre wavelength is 300 MHz.
A quarter-wave antenna is a quarter of the wavelength. Select the vacuum option and read the quarter-wavelength row.
Wavelength to frequency when you start from a physical length, such as a room dimension or an antenna. Frequency to wavelength when you start from a note or a band and want to know how big it is.
343 m/s covers dry air at 20 °C and is the default. Add roughly 0.6 m/s for every degree above that and subtract the same below, so a cold 5 °C loading bay is closer to 334 and a 30 °C room about 349.
A room resonates where a half wavelength fits a dimension. A 4 m wall supports a half wave of 4 m, so an 8 m wave, so about 43 Hz, and its multiples. Read the half-wavelength row against your room dimensions to find which notes will boom.