AC-05Acoustic Fundamentals
Wavelength & Frequency
How long is a sound wave? Wavelength, period and wavenumber in air, water and solids.
Inputs
Hz
°C
Wavelength λ
0.3432m
λ / 4
0.0858m
Period T
1ms
Wavenumber k
18.31rad/m
Speed of sound 343.2 m/s. One wavelength is about 1.6 × a football.
Pressure along the propagation axissnapshot, two wavelengths
Wavelength vs frequency
AirWaterSteel
§ Theory of operation
The wave equation in one line
For any travelling wave, speed equals frequency times wavelength:
\lambda = c\,/\,f \qquad T = 1\,/\,f \qquad k = 2\pi\,/\,\lambda = \omega\,/\,c
In air at 20 °C (c ≈ 343 m/s), audible sound spans an astonishing range: about 17 m at 20 Hz down to 17 mm at 20 kHz, a factor of 1000. This is why acoustics behaves so differently across the spectrum.
Why wavelength matters
- Absorbers: a porous absorber works well once its thickness approaches λ/4. Effective bass absorption therefore needs deep treatment or resonant absorbers.
- Barriers and diffraction: obstacles small compared with λ are transparent to sound; low frequencies bend around walls and buildings.
- Room modes appear when a room dimension equals a multiple of λ/2.
- Microphone spacing in intensity probes and arrays must be small compared with λ to avoid spatial aliasing.
- Near field: close to a source (within about λ/2π or the source size) pressure and velocity are not in phase and the inverse-square law does not yet apply.
Solids and liquids
Sound travels faster in stiffer media, so wavelengths are longer: a 1 kHz longitudinal wave in steel is almost 6 m long. Note that plates and beams also carry slower, dispersive bending waves whose speed rises with √f, see the panel transmission-loss calculator.