Sound Wavelength Calculator
Enter any two of frequency, wavelength, or speed of sound and the third is calculated instantly. Choose from 13 material presets - air at 0 and 20 degrees Celsius, water at three temperatures, glass, steel, aluminum, helium and more - or enter a custom speed. Results include the wave period, angular wave number, and context on where the frequency sits in the human and animal hearing spectrum.
Formula
Worked example
Middle A (concert pitch, 440 Hz) in air at 20 degrees Celsius (v = 343 m/s): lambda = 343 / 440 = 0.7795 m (about 78 cm). The period is T = 1/440 = 2.27 ms and the wave number is k = 2pi/0.7795 = 8.06 rad/m.
The wave equation for sound
Sound travels as a longitudinal pressure wave through any material medium - it cannot propagate through a vacuum. The fundamental relationship between wavelength, frequency and speed is the wave equation: lambda = v / f. Wavelength (lambda, in metres) is the physical distance between two successive compressions or rarefactions of the medium. Frequency (f, in hertz) is how many complete cycles pass a fixed point each second. Speed (v, in metres per second) depends almost entirely on the medium and its temperature, not on the frequency. Doubling the frequency halves the wavelength; doubling the speed doubles the wavelength - the frequency stays set by whatever is producing the sound.
How the speed of sound changes with medium and temperature
Sound travels faster in stiffer, denser media. In gases the speed is controlled by the ratio of the gas's bulk modulus to its density, which gives the well-known result that speed in air rises by about 0.6 m/s for every 1-degree Celsius rise in temperature. In dry air the formula is v = 331 + 0.6 T (metres per second, where T is Celsius). That is why sound is about 6% faster on a hot summer day (35 degrees C, roughly 352 m/s) than on a freezing morning (0 degrees C, 331 m/s). Liquids carry sound faster than gases because they are far less compressible: water at room temperature transmits sound at about 1 481 m/s, more than four times faster than air. Solids are stiffer still: aluminum and steel carry sound at 6 000 m/s or more. Helium, though a gas, is much lighter than air and carries sound at nearly 3 times the speed, which is why breathing helium makes voices sound high-pitched (the resonant frequencies of the vocal tract shift upward because the wave speed is higher).
Period, wave number and other derived quantities
This calculator also gives you the period (T) and the angular wave number (k). The period is the time for one complete oscillation: T = 1 / f. At 440 Hz the period is about 2.27 milliseconds - less than the blink of an eye. The angular wave number k = 2 pi / lambda describes the spatial frequency of the wave: how many radians of phase shift occur per metre of travel. Both quantities appear in the full wave equation y(x,t) = A sin(kx - omega t), where omega = 2 pi f is the angular frequency. Understanding k and T is useful in acoustics, signal processing, room design and musical instrument physics.
Human and animal hearing ranges
The human auditory system responds to frequencies from about 20 Hz to 20 000 Hz (20 kHz). Below 20 Hz lies infrasound, produced by earthquakes, large machinery and weather events; you may feel these frequencies as vibrations without hearing them as tones. Above 20 kHz lies ultrasound. Dogs and cats can hear up to roughly 40-85 kHz, bats use frequencies up to 160 kHz for echolocation, and dolphins extend beyond 150 kHz. Medical ultrasound imaging typically uses 1-20 MHz, where wavelengths in tissue fall to fractions of a millimetre, enabling sharp images. The audible wavelength range in air at 20 degrees Celsius spans from about 17 m at 20 Hz down to 17 mm at 20 kHz. Concert hall acoustics are strongly influenced by wavelength: low bass notes whose wavelengths exceed room dimensions diffract freely around obstacles, while treble notes whose wavelengths are small compared to a seat or pillar can be blocked or reflected.
Speed of sound in common media
| Medium | Temperature | Speed (m/s) | Notes |
|---|---|---|---|
| Air | 0 °C | 331 | Dry air at sea level |
| Air | 20 °C | 343 | Standard room conditions |
| Helium | 20 °C | 972 | Much lighter than air |
| Hydrogen | 20 °C | 1270 | Lightest gas |
| Water | 0 °C | 1402 | Cold fresh water |
| Water | 20 °C | 1481 | Room-temperature water |
| Water | 100 °C | 1543 | Near-boiling fresh water |
| Rubber | 20 °C | 1600 | Varies by hardness |
| Lead | 20 °C | 2160 | Very dense metal |
| Wood | 20 °C | 3850 | Average across species |
| Glass | 20 °C | 5640 | Typical silica glass |
| Aluminum | 20 °C | 6420 | Lightweight structural metal |
| Steel | 20 °C | 5960 | Carbon steel |
Reference values at the indicated temperatures. Denser or stiffer materials generally carry sound faster.
Frequently asked questions
What is the wavelength of sound at 440 Hz?
In air at 20 degrees Celsius (speed of sound 343 m/s), a 440 Hz tone - concert-pitch middle A - has a wavelength of 343 / 440 = 0.7795 m, about 78 cm. In water at 20 degrees the same frequency has a wavelength of 1 481 / 440 = 3.37 m because sound travels over four times faster in water.
Does the speed of sound change with frequency?
In air and most homogeneous media, no - sound speed is essentially independent of frequency, which is why music from a distant source sounds undistorted. The effect is called non-dispersion. In certain structured or highly viscous materials, different frequencies can travel at slightly different speeds (dispersion), but for practical acoustics in air or water the wave equation lambda = v / f treats v as a constant for all frequencies.
Why is the speed of sound so much faster in steel than in air?
Speed depends on the ratio of the medium's stiffness (bulk or Young's modulus) to its density. Steel is roughly 1 000 000 times stiffer than air, and although it is also about 7 000 times denser, stiffness wins: sound in steel travels at about 5 960 m/s compared to 343 m/s in air - nearly 17 times faster.
What does the wave number tell me?
The angular wave number k = 2 pi / lambda describes how rapidly the wave oscillates in space, in units of radians per metre. A large k (short wavelength) means the wave changes phase quickly over a short distance. It appears alongside the angular frequency omega in the full wave expression y(x,t) = A sin(kx - omega t), and it is widely used in physics, audio engineering and sonar calculations.
What is infrasound and why is it hard to hear?
Infrasound refers to sound waves below about 20 Hz - the lower limit of human hearing. At these frequencies the wavelengths in air exceed 17 m. The human ear's outer structure and eardrum are poorly matched to such long waves, so the mechanical coupling is inefficient. Very strong infrasound can still be felt as pressure or vibration. Natural sources include earthquakes, volcanic eruptions, ocean waves and large storms; some animals, such as elephants, use infrasound for long-distance communication.