Period Formulas
Period–Frequency Relationship
Period and frequency are inverse quantities. Double the frequency and the period halves. This reciprocal relationship T = 1/f is one of the most fundamental in physics.
You can also find the period from wavelength and wave speed: T = λ/v. Since v = fλ, substituting gives T = λ/(fλ) = 1/f, confirming consistency.
Common Periods in Nature and Engineering
| Phenomenon | Frequency | Period |
|---|---|---|
| Earth's rotation | 1.16 × 10⁻⁵ Hz | 86,400 s (24 h) |
| Resting heartbeat | ~1.2 Hz | ~0.83 s |
| 1-metre pendulum | ~0.5 Hz | ~2.0 s |
| AC mains (50 Hz) | 50 Hz | 20 ms |
| Middle C (261.6 Hz) | 261.6 Hz | 3.82 ms |
| CPU clock (3 GHz) | 3 GHz | 0.33 ns |
| Visible light | 430–790 THz | 1.3–2.3 fs |
Worked Examples
50 Hz AC Mains
T = 1/f = 1/50 = 0.02 s = 20 ms. The voltage completes one full sinusoidal cycle every 20 milliseconds.
Engine at 3000 RPM
T = 60/3000 = 0.02 s = 20 ms per revolution. f = 50 Hz, ω = 314.2 rad/s.
Sound wave: λ = 0.5 m in air
T = λ/v = 0.5/343 ≈ 1.46 × 10⁻³ s ≈ 1.46 ms (f ≈ 686 Hz).
Where Period Matters
| Field | Why Period Matters |
|---|---|
| Music & Acoustics | Period determines pitch; tuning instruments requires matching periods |
| Electrical Engineering | AC waveform period determines timing, sampling rates, and filter design |
| Mechanical Engineering | Vibration period identifies resonance frequencies in structures |
| Astronomy | Orbital period of planets, pulsars, binary stars |
| Digital Electronics | Clock period sets processor timing; T = 1/clock_frequency |
Limitations
This calculator assumes ideal periodic oscillations. Real-world signals may have varying periods (frequency drift), non-sinusoidal waveforms (which contain harmonics), or damped oscillations where period changes over time. The RPM mode assumes constant rotational speed.
Frequently Asked Questions
What is the period of a wave?›
The period (T) is the time required for one complete cycle of a wave or oscillation. It is the reciprocal of frequency: T = 1/f. If a wave has a frequency of 100 Hz, its period is 1/100 = 0.01 seconds (10 milliseconds).
How are period and frequency related?›
Period and frequency are reciprocals: T = 1/f and f = 1/T. Doubling the frequency halves the period, and vice versa. This inverse relationship is fundamental to all periodic phenomena.
What is the period of visible light?›
Visible light oscillates extremely fast. For red light (f ≈ 430 THz), the period is about 2.3 × 10⁻¹⁵ seconds (2.3 femtoseconds). For violet light (f ≈ 790 THz), the period is about 1.3 femtoseconds.
How do you convert RPM to period?›
T = 60/RPM. For example, 3000 RPM = 60/3000 = 0.02 seconds per revolution. RPM (revolutions per minute) is common in mechanical engineering for motors, engines, and turbines.
What is the difference between period and wavelength?›
Period is the time for one cycle (measured in seconds). Wavelength is the spatial distance for one cycle (measured in metres). They are related through wave speed: λ = v × T, or T = λ/v.
What is angular frequency?›
Angular frequency (ω) measures oscillation in radians per second: ω = 2πf. The period is T = 2π/ω. It simplifies mathematical expressions in physics, especially for circular motion and wave equations.
What is the period of 50 Hz and 60 Hz AC power?›
50 Hz AC has a period of 1/50 = 0.02 s (20 ms). 60 Hz AC has a period of 1/60 ≈ 0.0167 s (16.7 ms). These are the two standard mains frequencies used worldwide.
Can the period be negative or zero?›
No. Period is a positive quantity representing a duration. A period of zero would imply infinite frequency, and negative periods have no physical meaning.
