Wavelength to Frequency Calculator

Calculate frequency from wavelength and wave velocity across different mediums

Wave Properties Calculator

Electromagnetic waves in vacuum

Speed of wave propagation in the medium

Distance between adjacent wave peaks

Calculation Results

500.000 nm
Wavelength (λ)
599.585 THz
Frequency (f)
299.792 Mm/s
Wave Velocity (v)
1.668e-15 s
Period (T)
(T = 1/f)
5.996e+14 rad/s
Angular Frequency
(ω = 2πf)
1.257e+7 m⁻¹
Wave Number
(k = 2π/λ)
2.480 eV
Photon Energy
(E = hf)
3.973e-19 J
Photon Energy (J)
Planck's equation

Electromagnetic Spectrum

Visible Light

Frequency Range: 430 - 750 THz

Formula used: f = v / λ

Wave equation: v = f × λ (velocity = frequency × wavelength)

Example Calculations

Light Wave in Vacuum

Given: Wavelength = 500 nm, Velocity = 299,792,458 m/s

Formula: f = v / λ

Calculation: f = 299,792,458 m/s ÷ (500 × 10⁻⁹ m)

Result: f = 5.996 × 10¹⁴ Hz = 599.6 THz

Analysis: Green light frequency in visible spectrum

Sound Wave in Air

Given: Wavelength = 20 m, Velocity = 343 m/s (20°C)

Calculation: f = 343 m/s ÷ 20 m

Result: f = 17.15 Hz

Analysis: Low frequency sound, barely audible

Radio Wave

Given: Frequency = 100 MHz, Velocity = 299,792,458 m/s

Calculation: λ = v / f = 299,792,458 ÷ (100 × 10⁶)

Result: λ = 2.998 m

Analysis: FM radio wavelength

Common Wave Velocities

Wave TypeVelocity
Light (Vacuum)2.998 × 10⁸ m/s
Light (Air)2.997 × 10⁸ m/s
Light (Water)2.25 × 10⁸ m/s
Sound (Air, 20°C)343 m/s
Sound (Water)1,481 m/s
Sound (Steel)5,960 m/s
Seismic P-wave6,000 m/s
Ocean Waves~15 m/s

EM Spectrum Frequency Ranges

Radio Waves

3 kHz - 300 GHz

Broadcasting, communications

Microwaves

300 MHz - 300 GHz

Cooking, radar, satellite

Infrared

300 GHz - 430 THz

Heat radiation, thermal imaging

Visible Light

430 - 750 THz

Human vision, photosynthesis

UV / X-rays / Gamma

> 750 THz

Medical imaging, sterilization

Wave Equations

Basic Wave Equation

v = f × λ

velocity = frequency × wavelength

Period and Frequency

T = 1/f

period = 1/frequency

Angular Frequency

ω = 2πf

radians per second

Wave Number

k = 2π/λ

spatial frequency

Understanding Wavelength and Frequency

Wave Fundamentals

Wavelength and frequency are fundamental properties of all waves, whether they are electromagnetic waves like light and radio, or mechanical waves like sound and water waves. These properties are inversely related through the wave velocity.

Key Relationships

  • Higher frequency = shorter wavelength (at constant velocity)
  • Wave velocity depends on the medium properties
  • Electromagnetic waves travel fastest in vacuum

Wave Types and Applications

Different types of waves have different velocity ranges and applications. Understanding these relationships is crucial for fields ranging from telecommunications to medical imaging and astronomical observations.

Medium Effects

Electromagnetic: Slower in denser media (higher refractive index)
Sound: Faster in denser media (higher bulk modulus)
Water Waves: Velocity depends on wavelength and depth
Seismic: Velocity changes with rock density and composition

Practical Applications

Communications

  • • Radio and TV broadcasting
  • • Mobile phone frequencies
  • • WiFi and Bluetooth
  • • Satellite communications

Medical Applications

  • • Ultrasound imaging
  • • X-ray diagnostics
  • • MRI scanning
  • • Laser therapy

Scientific Research

  • • Spectroscopy analysis
  • • Astronomical observations
  • • Material characterization
  • • Seismic monitoring

Real-World Examples

Electromagnetic Spectrum

  • • AM Radio: ~1 MHz, ~300 m wavelength
  • • FM Radio: ~100 MHz, ~3 m wavelength
  • • Microwave Oven: 2.45 GHz, ~12 cm wavelength
  • • Visible Light: ~500 THz, ~600 nm wavelength

Sound and Mechanical Waves

  • • Human Speech: 300-3000 Hz in air
  • • Musical Note A4: 440 Hz, ~78 cm in air
  • • Ultrasound Medical: 2-18 MHz in tissue
  • • Earthquake P-waves: 0.1-10 Hz in rock