Wave Properties Calculator

Calculate wave frequency, wavelength, and wave speed using the fundamental wave equation: v = f × λ. Works for all types of waves.

About Wave Properties

The Wave Equation

The fundamental relationship between wave speed (v), frequency (f), and wavelength (λ) is: v = f × λ

This equation applies to all types of waves: mechanical waves (sound, water, seismic), electromagnetic waves (light, radio, X-rays), and matter waves.

Key Definitions

• Frequency (f): Number of wave cycles per second, measured in Hertz (Hz). Higher frequency = more oscillations per second.
• Wavelength (λ): Distance between successive wave crests, measured in meters. Longer wavelength = waves are more spread out.
• Wave Speed (v): How fast the wave propagates through the medium, measured in m/s.
• Period (T): Time for one complete cycle, T = 1/f.

Relationship Between Properties

• For a given wave speed: higher frequency → shorter wavelength
• For a given wave speed: lower frequency → longer wavelength
• Frequency and wavelength are inversely proportional when speed is constant

Wave Speeds in Different Media

• Light in vacuum: c = 299,792,458 m/s (≈ 3 × 10⁸ m/s)
• Sound in air (20°C): ≈ 343 m/s
• Sound in water: ≈ 1,480 m/s
• Sound in steel: ≈ 5,960 m/s
• Seismic waves: 3,000 - 8,000 m/s

Electromagnetic Spectrum

All electromagnetic waves travel at the speed of light (c) in vacuum:

• Radio waves: λ > 1 mm, f < 300 GHz
• Microwaves: λ = 1 mm - 1 m, f = 300 MHz - 300 GHz
• Infrared: λ = 700 nm - 1 mm, f = 300 GHz - 430 THz
• Visible light: λ = 400 - 700 nm, f = 430 - 750 THz
• Ultraviolet: λ = 10 - 400 nm, f = 750 THz - 30 PHz
• X-rays: λ = 0.01 - 10 nm, f = 30 PHz - 30 EHz
• Gamma rays: λ < 0.01 nm, f > 30 EHz

Applications

• Music & Acoustics: Musical notes have specific frequencies (A440 = 440 Hz)
• Radio & WiFi: Different frequencies for different services (FM, AM, WiFi, cellular)
• Optics: Color of light determined by wavelength
• Medical Imaging: Ultrasound frequency affects resolution and penetration depth
• Astronomy: Doppler shift of light wavelength reveals stellar motion