Frequency Converter

The highest frequency gamma rays detected come from astrophysical sources. The LHAASO observatory detected photons at about 1.4 PeV (1.4 × 10¹⁵ eV) from the Crab Nebula, corresponding to f = E/h ≈ 3.4 × 10²⁹ Hz. The theoretical upper limit is the Planck frequency f_P = 1/t_P = c/l_P = √(c⁵/ℏG) ≈ 1.86 × 10⁴³ Hz, above which quantum gravity effects dominate.

Atomic clocks use the stable frequency of atomic transitions as a reference. The primary standard is the caesium-133 hyperfine transition at exactly 9,192,631,770 Hz (by definition of the SI second). A caesium fountain clock counts exactly 9,192,631,770 microwave cycles to define one second, achieving stability of 10⁻¹⁵ (1 second error in 30 million years). Optical lattice clocks using strontium transitions at ~429 THz achieve 10⁻¹⁸ stability.

The Nyquist-Shannon theorem states that to digitally sample a signal without aliasing, the sampling frequency must be at least twice the highest frequency in the signal: f_sample ≥ 2f_max (Nyquist rate). CD audio samples at 44,100 Hz to capture frequencies up to 22,050 Hz (above human hearing limit of ~20 kHz). Digital radio (DAB) uses 48 kHz; professional audio 96-192 kHz; ultrasonic imaging 40-80 MHz.

Resonance occurs when a driving frequency matches a system's natural frequency, leading to large-amplitude oscillations. For a simple spring-mass system: f₀ = √(k/m)/(2π). For an LC circuit: f₀ = 1/(2π√(LC)). The Tacoma Narrows Bridge collapsed in 1940 when wind-induced oscillations matched the bridge's natural frequency (~0.2 Hz). Radio tuning works by adjusting LC resonance to match the desired broadcast frequency.

5G uses three frequency bands: Sub-1 GHz (600-900 MHz) for wide coverage, low data rates; Sub-6 GHz (1-6 GHz, especially 2.5, 3.5 GHz) for balanced coverage and speed; mmWave (24-40 GHz, especially 28 and 39 GHz) for ultra-high speed (10+ Gbps) but very limited range (~100 m). The millimeter-wave bands have wavelengths of 5-15 mm, explaining their poor penetration through walls and rain.

The electron cyclotron resonance (ECR) frequency is f_ce = eB/(2πm_e) = 27.99 GHz/T. At Earth's magnetic field (~50 μT): f_ce ≈ 1.4 MHz. In the ionosphere (50-100 μT): f_ce ≈ 1.4-2.8 MHz, affecting radio wave propagation. In laboratory plasma sources at B = 87.5 mT: f_ce = 2.45 GHz — the same as a microwave oven! This is used in ECR ion sources to efficiently ionize gases for particle accelerators and semiconductor etching.

EEG brain waves by frequency band: delta (0.5-4 Hz, deep sleep); theta (4-8 Hz, drowsiness, meditation); alpha (8-13 Hz, relaxed awareness); beta (13-30 Hz, active thinking); gamma (30-100 Hz, cognitive processing, attention). The MEG (magnetoencephalography) uses SQUID sensors to detect the weak magnetic fields (1-500 fT) produced by neural currents at these EEG frequencies.

Terahertz (THz) radiation (0.1-10 THz, 30 μm-3 mm wavelength) occupies the 'THz gap' between microwave electronics and optical photonics. Photon energies 0.4-40 meV make it sensitive to molecular rotation/vibration spectra. Applications: security screening (THz images show weapons under clothing without ionizing radiation health risks), pharmaceutical quality control, non-destructive testing, and 6G communications research.

Visible light frequencies: red 430-480 THz (700-625 nm); orange 480-510 THz (625-590 nm); yellow 510-530 THz (590-565 nm); green 530-600 THz (565-500 nm); blue 600-680 THz (500-440 nm); violet 680-750 THz (440-400 nm). The photon energy range is 1.77-3.10 eV. The exact boundaries vary by observer; colorblind individuals have missing or shifted cone photoreceptor response curves.