Period (wave)
The period of a wave is the time taken for one complete wave cycle to pass a fixed point, measured in seconds. It is the reciprocal of frequency: T = 1/f. Period is important in analysing oscillating systems such as pendulums, AC circuits, and vibrating strings, where knowing the cycle time allows calculation of frequency and wave speed.
Key Formula
T = 1 / f
LaTeX: T = \dfrac{1}{f}
| Symbol | Meaning | Unit |
|---|---|---|
| T | Period | s |
| f | Frequency | Hz |
Worked Example
Problem
A sound wave has a frequency of 440 Hz (the note A4). What is its period?
Solution
Step 1: Use T = 1 / f. Step 2: Substitute — T = 1 / 440. Step 3: Calculate — T ≈ 0.00227 s.
Answer
T ≈ 2.27 × 10⁻³ s (2.27 ms)
Period and Frequency of Common Waves
| Wave / Source | Frequency (Hz) | Period (s) | Category |
|---|---|---|---|
| Human heartbeat | 1.2 | 0.83 | Biological |
| Middle C (music) | 261.6 | 0.00382 | Sound |
| FM radio (98 MHz) | 9.8 × 10⁷ | 1.02 × 10⁻⁸ | Radio |
| AC mains (India) | 50 | 0.02 | Electrical |
| Visible green light | 5.5 × 10¹⁴ | 1.8 × 10⁻¹⁵ | Electromagnetic |
Interactive Tools
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Related Terms
Frequency
Frequency is the number of complete wave cycles that pass a fixed point per unit time, measured in hertz (Hz), where 1 Hz equals one cycle per second. It determines the pitch of a sound (higher frequency = higher pitch) and the colour of light (higher frequency = more energetic, bluer light). Frequency is inversely proportional to the wave period: f = 1/T.
Wavelength
Wavelength is the spatial distance between two consecutive points that are in the same phase of a wave, such as crest to crest or trough to trough. It is denoted by the Greek letter lambda (λ) and measured in metres. Wavelength is inversely related to frequency: higher-frequency waves have shorter wavelengths, which is why X-rays (short λ) are more energetic than radio waves (long λ).
Wave
A wave is a disturbance that transfers energy through a medium or through space without permanently displacing the medium itself. Waves are fundamental to how energy propagates in nature, from ocean ripples to light traveling across the universe. They are characterised by properties such as wavelength, frequency, amplitude, and speed, and underpin technologies ranging from radio communication to medical ultrasound.
From Latin "periodus" and Greek "periodos" (circuit, cycle), from "peri" (around) + "hodos" (way, path). Adopted into physics to denote the time of one complete oscillation.