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Wave Speed
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Sources & Methodology
Speed of light from NIST CODATA (exact: 299,792,458 m/s). Speed of sound formula from NIST. Wave speeds in materials from standard engineering references.
NIST CODATA — Speed of Light c = 299,792,458 m/s
Exact defined value of the speed of light in vacuum. Speed of sound in air temperature formula (331.3 + 0.606T m/s) from NIST acoustic reference data, used for the media reference table.
NIST SP 811 — SI Units: Metre, Second, Hertz
SI unit definitions for wave speed (m/s), wavelength (m), and frequency (Hz) used in the wave equation v = lambda times f in this calculator.
Methodology: v = λ×f. λ = v/f. f = v/λ. Period T = 1/f = λ/v. Wavenumber k = 2π/λ. Mach number = v/343 (at 20°C). Sound in air: v = 331.3 + 0.606×T m/s (T in °C). Speed of light in medium: v = c/n (n = refractive index). All three variables are algebraic rearrangements of the same fundamental wave equation.
⏱ Last reviewed: April 2026
How to Calculate Wave Speed — Formula and Reference
Every wave obeys the universal wave equation v = λ×f. If you know any two of the three quantities (speed, wavelength, frequency), you can find the third. The wave speed is set by the medium, not the frequency — all audible sound travels at 343 m/s in air at 20°C regardless of pitch.
The Wave Equation
v = λ × f λ = v / f f = v / λ
Verify sound of A4: λ = 0.780 m, f = 440 Hz → v = 0.780 × 440 = 343.2 m/s ✓
FM radio: λ = 3 m, f = 100 MHz → v = 3 × 10⁸ = 3.0×10⁸ m/s ≈ c ✓
Medical US: f = 5 MHz, v = 1540 m/s (tissue) → λ = 1540/5×10⁶ = 0.308 mm
FM radio: λ = 3 m, f = 100 MHz → v = 3 × 10⁸ = 3.0×10⁸ m/s ≈ c ✓
Medical US: f = 5 MHz, v = 1540 m/s (tissue) → λ = 1540/5×10⁶ = 0.308 mm
Wave Speed in Different Media
| Medium | Wave Type | Speed (m/s) | Notes |
|---|---|---|---|
| Vacuum | EM / Light / Radio | 299,792,458 | Exact, by SI definition |
| Glass (n=1.5) | Light | 199,862,000 | c/1.5 |
| Water (n=1.33) | Light | 225,409,000 | c/1.33 |
| Air at 0°C | Sound | 331 | v = 331.3 + 0.606T |
| Air at 20°C | Sound | 343 | Standard reference |
| Air at 40°C | Sound | 355 | Hot conditions |
| Fresh water (20°C) | Sound | 1480 | 4.3× faster than air |
| Seawater (20°C) | Sound | 1520 | Salt increases speed |
| Human soft tissue | Ultrasound | 1540 | Medical ultrasound standard |
| Aluminium | Sound (longitudinal) | 6420 | Nondestructive testing |
| Steel | Sound (longitudinal) | 5100–5900 | Alloy-dependent |
| Granite (seismic) | P-wave | 5000–6000 | Earthquake location |
💡 Wave speed is a property of the medium, not the wave. In air at 20°C, all audible frequencies (20 Hz–20 kHz) travel at exactly 343 m/s. In dispersive media like glass, different light wavelengths travel at slightly different speeds — this is what separates white light into a rainbow spectrum through a prism. Ocean waves are also dispersive: longer wavelength swells travel faster than short choppy waves.
Frequently Asked Questions
v = λ×f. Wave speed equals wavelength times frequency. For sound A4 at 440 Hz with λ = 0.780 m: v = 0.780 × 440 = 343.2 m/s. For FM radio at 100 MHz with λ = 3 m: v = 3 × 10⁸ = 3.0×10⁸ m/s (speed of light). Rearranging: λ = v/f and f = v/λ.
343 m/s at 20°C = 1235 km/h. Formula: v = 331.3 + 0.606×T m/s (T in °C). At 0°C: 331 m/s. At 40°C: 355 m/s. At −30°C: 313 m/s. Sound speed in air does not depend on frequency, loudness, or barometric pressure at constant temperature. Humidity slightly increases it.
v = √(K/ρ) where K = bulk modulus (stiffness) and ρ = density. Water’s bulk modulus is ~15,000 times greater than air, while its density is only ~800 times greater. Net effect: water transmits sound ~4.3 times faster (1480 vs 343 m/s). Steel is stiffer still, giving ~5900 m/s.
λ = v/f. For sound at 343 m/s and 1000 Hz: λ = 0.343 m = 34.3 cm. For medical ultrasound at 1540 m/s and 5 MHz: λ = 1540/(5×10⁶) = 0.308 mm. For radio at c and 100 MHz: λ = 2.998×10⁸/10⁸ = 2.998 m. Shorter wavelength means better spatial resolution in imaging.
In non-dispersive media (air for audible sound, vacuum for EM), wave speed is independent of frequency. All audible frequencies travel at 343 m/s in air. In dispersive media (glass for light, deep water for ocean waves), speed changes with frequency. Deep water wave speed: v ≈ √(gλ/(2π)) — longer ocean waves travel faster.
Mach 1 = local speed of sound = 343 m/s at 20°C = 1235 km/h = 767 mph. Mach number = v/v_sound. At high altitude (−50°C), speed of sound = 299 m/s so Mach 1 is slower in absolute terms. Concorde cruised at Mach 2.02 = 2179 km/h. SR-71 Blackbird: Mach 3.2 = 3780 km/h.
c = 299,792,458 m/s. Sound in air = 343 m/s. Ratio: c/v_sound = 873,850 times faster. Light circles Earth in 0.13 seconds; sound takes 32.7 hours. This 873,850× difference explains the thunder delay after lightning: every 3 seconds of delay = about 1 km distance from the lightning strike (343 m/s × 3 s = 1029 m ≈ 1 km).
v = 331.3 + 0.606T m/s (T in °C). For each 1°C rise, sound speed increases 0.606 m/s. Difference between −10°C (winter, 325 m/s) and 30°C (summer, 349 m/s) is 24 m/s (7.4%). This matters for sonar, acoustic delay lines, outdoor public address systems, and audio measurement equipment.
P-waves (primary, compressional) in granite: 5000–6000 m/s. S-waves (shear) in granite: ~3200 m/s (about 60% of P). Through Earth’s mantle: P-waves 8000–14000 m/s. S-waves cannot travel through the liquid outer core. Surface Rayleigh waves: 2000–4000 m/s. Seismologists locate earthquakes by measuring arrival time differences between P and S waves at multiple stations.
Deep water: v ≈ √(g×λ/(2π)). For λ = 100 m: v = √(9.81×100/6.283) = 12.5 m/s = 45 km/h. For λ = 1000 m: v = 39.5 m/s = 142 km/h. Tsunami in open ocean (λ >> depth): v = √(g×depth). At 4000 m depth: v = √(9.81×4000) = 198 m/s = 713 km/h. Longer wavelengths travel faster in deep water (dispersion).
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