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Calculate wave frequency (f), wavelength (λ), or wave speed (v) using the fundamental wave equation v = fλ. Covers sound waves, light, radio waves, and the complete electromagnetic spectrum with real-world applications.
All waves obey the fundamental equation: v = f × λ, where v is wave speed, f is frequency, and λ is wavelength. Frequency and wavelength are inversely related — higher frequency means shorter wavelength at constant speed. This applies to all wave types: sound, light, radio, X-rays.
Waves are periodic disturbances that transfer energy without permanently displacing matter. All waves — from sound to light to seismic waves — share fundamental properties: frequency (f, cycles per second = Hertz), wavelength (λ, distance between identical points), wave speed (v), amplitude (maximum displacement), and period (T = 1/f, time for one complete cycle). These properties are related by the fundamental wave equation: v = f × λ.
Wave speed depends on the medium, not the frequency. Sound travels at 343 m/s in air at 20°C regardless of whether it is a low bass note or a high pitch. In water: 1,481 m/s. In steel: 5,120 m/s. Light in vacuum: always c = 299,792,458 m/s regardless of frequency — from radio waves to gamma rays. This constancy of c is a postulate of Einstein's Special Relativity.
| Wave Type | Wavelength | Frequency | Applications |
|---|---|---|---|
| Radio waves | >1 mm to km | 300 GHz to 3 Hz | Broadcasting, WiFi, cellular |
| Microwave | 1 mm to 1 m | 300 GHz to 300 MHz | Radar, cooking, 5G |
| Infrared | 700 nm to 1 mm | 430 THz to 300 GHz | Heat, remote controls, night vision |
| Visible light | 380-700 nm | 790-430 THz | Human vision |
| Ultraviolet | 10-380 nm | 30 PHz to 790 THz | Sunburn, sterilization |
| X-rays | 0.01-10 nm | 30 EHz to 30 PHz | Medical imaging, security |
| Gamma rays | <0.01 nm | >30 EHz | Nuclear decay, cancer therapy |
Sound is a longitudinal pressure wave requiring a medium. Speed in air: v = 331.3 + 0.606×T°C m/s. At 20°C: 343 m/s. At 0°C: 331 m/s. Human hearing range: 20 Hz - 20,000 Hz (20 kHz). Wavelengths in air: 20 Hz = 17.15m (bass), 1 kHz = 0.343m (mid), 20 kHz = 17mm (treble). Infrasound (<20 Hz): earthquakes, whale communication, wind turbines. Ultrasound (>20 kHz): medical imaging (1-15 MHz), industrial testing, bat echolocation (20-200 kHz), dog whistles (23-54 kHz). Doppler effect: moving source or observer shifts observed frequency: f_obs = f_source × (v±v_obs)/(v∓v_source). Ambulance approaching: higher pitch. Receding: lower pitch. This shift, applied to light, reveals galaxy recession speeds (cosmological redshift).
Visible light occupies 380-700 nm wavelength range: violet (380-450 nm), blue (450-495 nm), green (495-570 nm), yellow (570-590 nm), orange (590-620 nm), red (620-750 nm). Color perception is frequency-based: each frequency stimulates cone cells differently. Frequency determines color; amplitude determines brightness. Refraction: light slows in denser media (v = c/n, where n = refractive index). Air n=1.0003, water n=1.33, glass n=1.5, diamond n=2.42. Rainbows: different wavelengths refract at different angles in water droplets, separating white light into spectrum. Fiber optics: total internal reflection confines light within glass core — basis of modern internet communications at terabit/second data rates.
Always ensure units are consistent before calculating. This calculator uses SI units (International System): meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, Newtons (N) for force, Joules (J) for energy, Watts (W) for power, and Pascals (Pa) for pressure. When converting from other unit systems (imperial, CGS), convert all values before entering them into the calculator.
Gravitational acceleration on Earth: g = 9.81 m/s² (standard: 9.80665 m/s²). Speed of light in vacuum: c = 2.998×10⁸ m/s. Universal gravitational constant: G = 6.674×10⁻¹¹ N·m²/kg². Speed of sound in air at 20°C: 343 m/s. Atmospheric pressure at sea level: 101,325 Pa = 1 atm. These constants appear in virtually every branch of physics and engineering.
Physics calculations directly inform engineering safety standards. Stopping distance calculations (kinetic energy / braking force) set speed limits and vehicle safety requirements. Pressure calculations determine pipe and vessel wall thickness in plumbing and industrial equipment. Torque specifications on fasteners prevent structural failures. Centripetal acceleration limits guide road curve design and roller coaster safety. Every safety standard in transportation, construction, and consumer products has physics calculations at its foundation.