Wave Speed Calculator

Calculate wave speed using v = fλ. Solve for speed, frequency, or wavelength. Includes medium presets (sound, light), string wave speed √(T/μ), shallow and deep water wave formulas.

Hz
m
Wave Speed
—
Period —
Angular Frequency (ω) —
Extended More scenarios, charts & detailed breakdown ▾
Hz
m
Wave Speed (v)
—
Period (T) —
Professional Full parameters & maximum detail ▾
N
kg/m
m
m

Wave Speed by Medium

String Wave Speed v=√(T/μ) —
Shallow Water Wave Speed v=√(gh) —
Deep Water Wave Speed v=√(gλ/2π) —
Shallow Water Period —

How to Use This Calculator

  1. Enter frequency (Hz) and wavelength (m) to find wave speed.
  2. Switch to Find Frequency or Find Wavelength tabs to solve for the other variables.
  3. Use medium presets to instantly apply speed of sound or light in common materials.
  4. Switch to Professional for string, shallow-water, and deep-water wave speed formulas.

Formula

v = fλ  |  f = v/λ  |  λ = v/f

String: v = √(T/μ)  |  Shallow water: v = √(gh)  |  Deep water: v = √(gλ/2π)

Example

Example: A440 note — frequency 440 Hz, speed of sound 343 m/s. Wavelength = 343/440 = 0.780 m.

Frequently Asked Questions

  • Wave speed v = fλ, where f is frequency in Hz and λ (lambda) is wavelength in meters. Rearranging: f = v/λ and λ = v/f.
  • The speed of sound in air at 20°C is approximately 343 m/s. It varies with temperature: v ≈ 331 + 0.6T m/s where T is temperature in Celsius.
  • Sound travels approximately 1480 m/s in water — about 4.3 times faster than in air. It travels even faster in steel (~5960 m/s) due to higher elasticity.
  • For transverse waves on a string: v = √(T/μ), where T is tension in Newtons and μ (mu) is linear density (kg/m). Higher tension or lower mass per length = faster waves.
  • Shallow water (depth < λ/20): v = √(gh). Deep water (depth > λ/2): v = √(gλ/2π). Shallow-water waves depend on depth; deep-water waves depend on wavelength.

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Sources & References (5) ▾
  1. Wave Speed — HyperPhysics — Georgia State University HyperPhysics
  2. University Physics Vol 1, Ch 16: Waves — OpenStax
  3. Wave Physics — NASA Science — NASA
  4. MIT OCW 8.03: Physics III — Vibrations and Waves — MIT OpenCourseWare
  5. Ocean Wave Theory — NOAA — NOAA Ocean Service