Calculate sound wavelength from frequency or vice versa. Supports 9 media (air, water, steel, etc.), temperature correction, musical note presets, and a multi-media comparison table.
Sound waves are longitudinal pressure oscillations that travel through a medium at a speed determined by the medium's properties. The fundamental relationship connecting wavelength (λ), frequency (f), and speed (v) is λ = v / f. Because the speed of sound varies dramatically between media — roughly 343 m/s in air, 1500 m/s in water, and 6000 m/s in steel — the same frequency produces very different wavelengths in different materials.
For musicians and audio engineers, knowing the wavelength is crucial for room acoustics, speaker placement, and microphone positioning. A 100 Hz bass note has a wavelength of about 3.4 m in air, while a 10 kHz treble note is only 3.4 cm — this explains why low frequencies diffract easily around obstacles while high frequencies are more directional.
This calculator computes wavelength from frequency (or frequency from wavelength) in any of 9 preset media, with temperature correction for air. Musical note presets let you quickly explore common frequencies, and the multi-media comparison table shows how the same sound behaves in different materials.
Converting between frequency and wavelength requires knowing the speed of sound in the specific medium, which changes with temperature and material. This calculator handles all the conversions, provides musical note presets for common frequencies, and compares wavelengths across 9 different media simultaneously — saving considerable reference lookup time. Keep these notes focused on your operational context.
Wavelength–Frequency Relation: λ = v / f f = v / λ Speed of Sound in Air: v ≈ 331.3 + 0.606 × T (m/s, T in °C) Period: T = 1 / f Wave Number: k = 2π / λ Where: v = speed of sound in the medium (m/s) λ = wavelength (m) f = frequency (Hz)
Result: λ = 0.780 m = 78.0 cm
At 20 °C, the speed of sound in air is v ≈ 331.3 + 0.606 × 20 = 343.4 m/s. For concert pitch A4 at 440 Hz: λ = 343.4 / 440 = 0.7805 m ≈ 78.0 cm. In water at the same frequency, the wavelength would be 1497 / 440 = 3.40 m — about 4.4 times longer.
The connection between frequency and wavelength is at the heart of musical instrument design. String instruments produce standing waves with wavelengths determined by the string length — a guitar string vibrating at its fundamental has a wavelength equal to twice the string length. Wind instruments use air column resonance, where the bore length determines the fundamental wavelength. Understanding these relationships helps musicians tune instruments and engineers design concert halls with optimal acoustics.
Sound behaves very differently in water than in air. The speed increase (roughly 4.4×) means wavelengths are proportionally longer for the same frequency. Submarine sonar operates at frequencies chosen to balance resolution (higher frequency, shorter wavelength) against range (lower frequency, less attenuation). The SOFAR channel — a layer in the ocean where sound speed is minimum — can trap sound waves and transmit them thousands of kilometers, a phenomenon used for undersea communication and monitoring.
At frequencies above 20 kHz, sound wavelengths become very short (millimeters or less in tissue), enabling applications from medical imaging to industrial non-destructive testing. Medical ultrasound typically operates at 2-18 MHz, producing wavelengths of 0.1-0.8 mm in tissue — fine enough to image organs, blood flow, and fetal development. Higher frequencies give better resolution but penetrate less deeply, requiring careful frequency selection for each application.
In gases, the speed of sound is proportional to the square root of absolute temperature: v = √(γRT/M). Higher temperature means faster molecular motion and faster sound propagation. In air, each degree Celsius adds about 0.6 m/s to the speed.
Humans typically hear from 20 Hz to 20,000 Hz (20 kHz). Below 20 Hz is infrasound (felt more than heard). Above 20 kHz is ultrasound (used in medical imaging and cleaning). Children can often hear up to 20 kHz; this range shrinks with age.
Waves diffract around obstacles comparable to or larger than their wavelength. Low-frequency sounds (long wavelength) bend around walls and furniture easily, while high frequencies (short wavelength) travel more directionally and are easily blocked. This is why you can hear bass through walls but treble is muffled.
Speed of sound depends on √(stiffness/density). Solids like steel are much stiffer than air, and even though they are denser, the stiffness increase dominates. Steel transmits sound at about 5960 m/s compared to 343 m/s in air.
The wave number k = 2π/λ describes how many radians of phase change occur per meter. It is essential in wave equations, interference calculations, and signal processing. In acoustics, it helps analyze standing waves, resonance, and acoustic impedance.
Yes, slightly. Humid air is actually less dense than dry air (water vapor is lighter than nitrogen and oxygen), so sound travels slightly faster in humid conditions — typically 0.1-0.5 m/s faster at normal humidity levels.