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
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
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
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