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Wave frequency (f) is the number of complete oscillations (cycles) per second, measured in Hertz (Hz). The fundamental wave equation f = v/λ connects frequency (f), wave speed (v), and wavelength (λ — the distance between consecutive peaks). Rearranging: v = fλ and λ = v/f. These three quantities are always linked — if you know any two, you can find the third.
Period T is the time for one complete cycle: T = 1/f. A wave at 100 Hz completes 100 cycles per second, so each cycle takes T = 1/100 = 0.01 seconds. For electromagnetic waves (light, radio, X-rays), the speed is c = 3×10⁸ m/s in vacuum, giving c = fλ. Visible light has frequencies 430–770 THz (wavelengths 390–700 nm).
In quantum physics, the energy of a photon is E = hf, where h = 6.626×10⁻³⁴ J·s is Planck's constant. Higher frequency means higher energy — this is why ultraviolet light causes sunburn and X-rays can penetrate tissue (high frequency, high energy), while radio waves are harmless (low frequency, low energy).
Worked example: An FM radio station broadcasts at 100 MHz (10⁸ Hz). Wavelength λ = c/f = (3×10⁸)/(10⁸) = 3 m. Period T = 1/f = 10⁻⁸ s = 10 nanoseconds. Photon energy E = hf = 6.626×10⁻³⁴ × 10⁸ ≈ 6.6×10⁻²⁶ J (very small, consistent with non-ionizing radiation).
f = v/λ | T = 1/f | E = h·f | c = f·λ
f = v / λ
Electromagnetic Spectrum Quick Reference
| Type | Frequency (Hz) | Wavelength (m) |
|---|---|---|
| Radio | < 3×10⁸ | > 1 m |
| Microwave | 3×10⁸ – 3×10¹¹ | 1 mm – 1 m |
| Infrared | 3×10¹¹ – 4×10¹⁴ | 700 nm – 1 mm |
| Visible Light | 4×10¹⁴ – 7.5×10¹⁴ | 400 – 700 nm |
| Ultraviolet (UV) | 7.5×10¹⁴ – 3×10¹⁶ | 10 – 400 nm |
| X-ray | 3×10¹⁶ – 3×10¹⁹ | 0.01 – 10 nm |
| Gamma ray | > 3×10¹⁹ | < 0.01 nm |
Speed of light in vacuum: c = 2.998×10⁸ m/s
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.