Wavelength Calculator
How long a sound wave is in air, either way round, at the temperature the air is actually at.
Wavelength
3.432 m
- Half wavelength
- 1.716 m
- Quarter wavelength
- 0.858 m
- One cycle lasts
- 10.000 ms
- Speed of sound used
- 343.2 m/s
Where this comes from
- Rule
- λ = c ÷ f, with c = √(γRT ÷ M) for dry air — γ 1.4, R 8.314462618 J·mol⁻¹·K⁻¹, M 0.02896546 kg·mol⁻¹
- Sources
- Caveat
- Dry air, at rest. Humidity raises the speed by under half a per cent at room temperature, which is finer than the measurement this answer is usually compared against.
A sound has a length as well as a pitch, and it is longer than most people expect: the bottom string of a bass guitar is over eight metres from one crest to the next. Knowing the figure is what tells you whether a room can be treated, where a microphone will cancel itself, and why the low end is the part that will not behave.
How it works
A wave travels one wavelength in one cycle, so the length is the speed divided by the frequency, and the frequency is the speed divided by the length. Either end of that gives the other.
The speed of sound is not a constant. It rises with temperature by about 0.6 metres per second per degree, so the same note is a few centimetres longer in a warm room than in a cold one. It is computed here from the relation for an ideal gas rather than read from a table, which is why the temperature is a field and why the speed used is shown with the answer.
The half and quarter wavelengths are given because they are the ones that get used. A room resonates where a half wavelength fits between two parallel walls, and a porous absorber works on a frequency whose quarter wavelength it is roughly as deep as — which is the arithmetic behind a bass trap being the size it is.
Examples
| Case | Input | Result |
|---|---|---|
| A low tone in a warm room | 100 Hz, 20 °C | 3.432 m |
Frequently asked questions
Why does the temperature matter?
Because sound moves through air, and warm air is less dense: the speed goes from 331 metres per second at freezing to 343 at twenty degrees. That is under four per cent, and on a three-metre wavelength it is more than a handspan — enough to matter when you are deciding where a wall treatment goes, and enough that a page printing 343 without asking would be quietly wrong outdoors.
Does humidity change the answer?
A little, and it is left out on purpose. Moist air carries sound slightly faster than dry air — under half a per cent in an ordinary room — which is finer than the tape measure the answer gets compared against. Asking for a humidity reading in order to move a figure by a centimetre would be precision for its own sake.
Is this the same for light or radio?
The relation is, the speed is not. Light and radio travel at 299 792 458 metres per second in a vacuum, nearly nine hundred thousand times faster than sound, so a radio wavelength comes out in metres for frequencies in megahertz. This tool is about sound in air, and says so rather than offering a medium menu that would make the wrong choice easy.
Why does my room resonate at those frequencies?
A pair of parallel walls resonates where half a wavelength fits between them, and again at every multiple of that. So a room four metres across has its first axial mode at about 43 Hz, then 86, then 129. Enter the length here as a wavelength and halve the frequency you get back to find the first one.
Good to know
- The speed of sound is computed, not looked up: from the ratio of specific heats of dry air, the molar gas constant and the molar mass of air. The check is that the same relation returns 331.3 metres per second at 0 °C and 343.2 at 20 °C — the two figures acoustics references print — without either being written into the code.
- Dry air at rest is what is modelled. Humidity, altitude and wind all shift the speed slightly and none of them is asked for, because each would cost a measurement you do not have in order to move the answer by less than you can measure.
- The temperature range offered stops at −60 and 60 °C. The arithmetic is happy outside it; an answer for air at 200 °C would be a physics exercise rather than a measurement anybody is taking.