Enter a frequency to find its wavelength, or enter a wavelength to find the corresponding frequency. Adjust temperature to account for changes in the speed of sound (warmer air = faster propagation = longer wavelength at the same frequency).
The ¼ wavelength value is the minimum depth a porous absorber (mineral wool, fibreglass) must be to absorb effectively at this frequency. This is why bass traps for 100 Hz need to be roughly 86 cm deep.
Reverse: wavelength → frequency
| Source | Frequency | Wavelength | ¼λ |
|---|
The Sound Wavelength Formula
Wavelength (λ) is the physical distance a sound wave travels during one complete cycle of oscillation. It is determined by the ratio of the propagation speed to the oscillation frequency:
λ = c / f
where c is the speed of sound in the medium and f is the frequency in hertz. In air, the speed of sound depends primarily on temperature:
c = 331.3 + 0.606 × T (m/s)
At 20 °C, c ≈ 343.4 m/s. This means a 1 kHz tone has a wavelength of about 34 cm, while a 50 Hz bass note stretches nearly 6.9 metres—longer than most rooms are wide. Humidity has a smaller effect (increasing speed by up to 0.5%) and is neglected here.
Why Wavelength Matters in Acoustics
Nearly every acoustic design decision depends on wavelength. The size of an absorber relative to the wavelength of sound it targets determines its effectiveness; the spacing of diffuser wells must relate to the wavelength range being scattered; speaker cabinet dimensions and port lengths are tuned in wavelength terms; and the room itself resonates when its dimensions are integer multiples of half a wavelength (see the Room Mode Calculator).
The fundamental reason low-frequency sound is so difficult to control is that its wavelength is comparable to, or larger than, the dimensions of the room and the treatment installed in it. A 100 Hz wave is 3.4 m long; a 4-inch acoustic panel is roughly 1/34 of that wavelength—acoustically transparent at that frequency.
Wavelength and Acoustic Treatment Sizing
Porous absorbers (fibreglass, mineral wool, open-cell foam) work by converting sound energy into heat through friction as air molecules oscillate within the material. Absorption is most effective when the absorber is located at a point of maximum particle velocity, which occurs at a distance of one-quarter wavelength from a rigid boundary (wall). This leads to the practical rule:
Minimum absorber depth ≈ λ/4 for effective absorption at frequency f.
- A 2-inch (5 cm) panel is effective down to roughly 1700 Hz.
- A 4-inch (10 cm) panel extends to roughly 850 Hz.
- A 6-inch (15 cm) panel with a 6-inch air gap extends to roughly 280 Hz.
- Full quarter-wavelength treatment at 80 Hz requires 107 cm of depth—impractical in most rooms, which is why corner-loading and membrane traps are used instead.
Audio Frequency Ranges and Wavelengths
| Range | Frequencies | Wavelengths | Acoustic character |
|---|---|---|---|
| Sub-bass | 20–60 Hz | 17.2–5.7 m | Felt more than heard; room modes dominate |
| Bass | 60–250 Hz | 5.7–1.4 m | Foundation; heavily affected by room dimensions |
| Low mids | 250–500 Hz | 1.4–0.69 m | Body and warmth; muddiness zone |
| Midrange | 500 Hz–2 kHz | 69–17 cm | Vocal intelligibility; most sensitive hearing range |
| Upper mids | 2–4 kHz | 17–8.6 cm | Presence and clarity; ear canal resonance (~3 kHz) |
| Presence | 4–6 kHz | 8.6–5.7 cm | Definition and articulation of consonants |
| Brilliance | 6–20 kHz | 5.7–1.7 cm | Air and sparkle; first to decline with age |
Speed of Sound in Different Media
Sound travels at different speeds depending on the medium’s density and elasticity. In denser, more rigid media, sound propagates faster. This calculator focuses on air, but for comparison:
- Air (20 °C): 343 m/s — wavelengths range from 17 m (20 Hz) to 1.7 cm (20 kHz).
- Water (25 °C): 1,497 m/s — wavelengths are 4.4× longer at the same frequency.
- Steel: 5,960 m/s — important for understanding structure-borne sound transmission.
- Concrete: ~3,400 m/s — relevant for building acoustics and impact noise.