Wave Speed, Frequency, Wavelength & Period Calculator

Wave Physics & Acoustics: The Fundamental Wave Equation

All periodic wave phenomena—including sound waves, water ripples, seismic waves, and electromagnetic light/radio waves—obey the universal kinematic relation:

• The Three Core Dimensions:

• Wave Speed (v, m/s): The velocity at which the wave disturbance transfers energy through the physical medium.

• Frequency (f, Hz): The number of complete wave cycles passing a fixed point per second (temporal oscillation rate).

• Wavelength (λ, meters): The physical spatial distance between two successive identical wave crests.

• Medium Invariance: When a wave transitions from one medium into another (e.g. light passing from air into glass), its frequency f remains strictly constant, while speed v and wavelength λ change proportionally).

• Quantum Duality: In quantum mechanics, de Broglie extended the wave equation to all matter particles), establishing that every moving electron and photon carries both wave and corpuscular properties.

How to Use This Calculator

Enter your Variable to Calculate — choose from Wavelength (λ = v / f) — Given Wave Speed & Frequency, Frequency (f = v / λ) — Given Wave Speed & Wavelength, Wave Speed (v = f · λ) — Given Frequency & Wavelength, Wave Medium Propagation Preset — choose from Sound in Air (20°C: 343 m/s), Electromagnetic Light / Radio in Vacuum (c = 299,792,458 m/s), Sound in Water (1,480 m/s), Wave Propagation Speed (v in m/s) (e.g. 343), Wave Frequency (f in Hz) (e.g. 440 (Concert Pitch A4: 440 Hz / Wi-Fi: 2.4e9 Hz)), and Wavelength (λ in meters) (e.g. 0.7795 (0.78 m = 78 cm)). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Universal Wave Equation \& Harmonic Wave equations:

v = f · λ = (λ) / (T)

f = (v) / (λ) = (1) / (T), λ = (v) / (f) = v · T

Angular Frequency: ω = 2 π f = (2π) / (T) (rad/s)

Angular Wavenumber: k = (2 π) / (λ) (rad/m)

Planck-Einstein Quantum Energy: E = h · f = (h · c) / (λ) (h = 6.62607 × 10^-34 J·s)

Worked Example

For example, evaluating an acoustic concert pitch A4 note) traveling through air at 20°C): Wavelength is . The wave period is . Angular frequency is \ = 2,764.60 rad/s, and wavenumber is .

Understanding Your Result

Kinematic reference values: Speed of light 3×10⁸ m/s (c), speed of sound in air at 20°C 343 m/s, speed of sound in water 1,480 m/s, Earth's orbital speed 29.8 km/s. Acceleration due to gravity (g) = 9.81 m/s² at sea level (varies 9.78 at equator to 9.83 at poles). Relativistic effects become measurable above ~10% of the speed of light — classical kinematic formulas apply for everyday speeds. Unit conversions: 1 m/s = 3.6 km/h = 2.237 mph.