Core answer: Frequency f (hertz) and period T (seconds) are reciprocals: f = 1/T. A 50 Hz mains cycle lasts 20 ms; a 2.4 GHz Wi-Fi wave cycles 2.4 billion times per second with period 0.42 ns. Music: concert A = 440 Hz, one octave up = 880 Hz — octaves DOUBLE frequency, they don't add.
The unit ladder
| Unit | Equals | Example |
|---|---|---|
| 1 Hz | 1 cycle/s | heartbeat ≈ 1.2 Hz |
| 1 kHz | 1,000 Hz | AM radio ~1 MHz, hearing to ~20 kHz |
| 1 MHz | 10⁶ Hz | FM radio 88–108 MHz |
| 1 GHz | 10⁹ Hz | Wi-Fi 2.4/5 GHz, CPUs |
| 1 THz | 10¹² Hz | visible light 430–750 THz |
Period ↔ frequency table
| f | T = 1/f | What |
|---|---|---|
| 50 Hz | 20 ms | China/EU mains |
| 60 Hz | 16.7 ms | US/Japan mains |
| 440 Hz | 2.27 ms | concert A |
| 1 kHz | 1 ms | audio reference |
| 2.4 GHz | 0.42 ns | Wi-Fi/Bluetooth |
| 60 rpm | 1 s | 1 rev per second |
Worked examples
Example 1 — Flicker. Old fluorescent lights on 50 Hz flicker at 100 Hz (both half-cycles) — below cinema's 24 fps fusion threshold it would strobe; modern LEDs with good drivers kill this.
Example 2 — Note frequencies. A4 = 440 Hz; C5 (middle C region) ≈ 523 Hz; each semitone multiplies by 2^(1/12) ≈ 1.0595. Twelve semitones = ×2 exactly = one octave.
Example 3 — CPU clock. A 3 GHz core executes ~3×10⁹ cycles/s; a 5-instruction task finishes in 5/3×10⁹ ≈ 1.7 ns — yet a RAM fetch costing ~100 ns dominates, which is why caches exist.
Example 4 — RPM to Hz. A car engine at 3,000 rpm = 50 rev/s = 50 Hz; a 4-cylinder 4-stroke fires 2× per rev → 100 Hz exhaust pulse at that speed.
Example 5 — Sampling. To capture 20 kHz audio you need > 40 kHz sampling (Nyquist); CDs chose 44.1 kHz with margin for filters.
Common mistakes and myths
- Confusing frequency with amplitude — frequency is pitch/speed; amplitude is loudness/size. A louder 50 Hz hum is still 50 Hz.
- Thinking octaves add — 440 + 440 = 880 happens to work numerically for the first octave, but the rule is multiplication: each octave doubles.
- "Higher GHz = always faster" — instructions per cycle, cores, and memory matter as much; a 2 GHz modern core beats a 3 GHz 2010 core.
- 5G confusion — "5 GHz Wi-Fi" (frequency) vs "5G cellular" (generation) are unrelated; 5G networks use 3.5 GHz / 4.9 GHz / mmWave bands in China.
- Assuming hearing is flat to 20 kHz — most adults top out at 14–16 kHz by age 40; mosquito ringtones exploit exactly this.