Waves and Frequency: Complete Guide
A wave is a disturbance that transfers energy through a medium (or through space for electromagnetic waves) without permanently displacing the material it travels through. Waves are everywhere: sound waves carry music, light waves bring images to your eyes, seismic waves ripple through Earth during earthquakes, and radio waves connect our devices.
All waves share common properties: amplitude (height of the disturbance), wavelength (spatial period), frequency (oscillations per second), period (time per oscillation), and speed. The fundamental wave equation v = fλ links speed, frequency, and wavelength — know any two and you can find the third.
Understanding waves is essential for acoustics, optics, telecommunications, medical imaging (ultrasound, MRI), and quantum mechanics (matter has wave-like properties described by de Broglie wavelength λ = h/p). This guide covers mechanical and electromagnetic waves and their key properties.
Formula
v = f·λ | T = 1/f | E = h·f (photons)
Wave Properties: Amplitude, Wavelength, Frequency, and Period
Amplitude (A) is the maximum displacement from the equilibrium position — the "height" of the wave. For sound waves, amplitude determines loudness (larger amplitude → louder sound). For light waves, amplitude determines brightness. Amplitude carries information about the energy of the wave: energy ∝ A².
Wavelength (λ) is the distance between two consecutive identical points on the wave (e.g., peak to peak, or trough to trough). It is the spatial period of the wave — the distance over which the wave pattern repeats. Units: metres (m), though nanometres (nm) are used for light and centimetres (cm) for microwaves.
Frequency (f) is the number of complete wave cycles per second, measured in Hertz (Hz). A 440 Hz sound wave completes 440 oscillations every second. Frequency is determined by the source of the wave and does not change when a wave passes from one medium to another (unlike speed and wavelength, which both change).
Period (T) is the time for one complete oscillation: T = 1/f. A 50 Hz mains electricity supply has T = 1/50 = 0.02 s = 20 ms per cycle. Period and frequency are reciprocals — knowing one gives the other immediately.
Frequency, Period, and the Wave Equation
The wave equation v = fλ is the fundamental relationship connecting wave speed, frequency, and wavelength. It applies to all types of waves. Rearranging: f = v/λ and λ = v/f. For a given medium (fixed v), higher frequency means shorter wavelength and vice versa — they are inversely proportional.
For electromagnetic waves in vacuum: v = c = 3×10⁸ m/s. Visible red light at f = 430 THz has wavelength λ = 3×10⁸/(4.3×10¹⁴) = 698 nm. Violet light at f = 750 THz has λ = 400 nm. Radio waves at f = 100 MHz have λ = 3 m. All travel at c; only wavelength and frequency differ.
For sound in air at 20°C: v ≈ 343 m/s. Middle C (f = 261.6 Hz) has λ = 343/261.6 ≈ 1.31 m. A dog whistle at 25,000 Hz has λ = 343/25,000 = 0.0137 m = 13.7 mm. Shorter wavelength sound is harder to detect because it diffracts less around obstacles.
| Wave type | Speed | Frequency range | Examples |
|---|---|---|---|
| Radio waves (EM) | 3×10⁸ m/s | < 300 MHz | AM/FM radio, TV broadcasts, WiFi |
| Microwaves (EM) | 3×10⁸ m/s | 300 MHz – 300 GHz | Microwave ovens, radar, 5G |
| Infrared (EM) | 3×10⁸ m/s | 300 GHz – 430 THz | Heat lamps, remote controls, thermal imaging |
| Visible light (EM) | 3×10⁸ m/s | 430 – 770 THz | Human vision (violet to red) |
| Ultraviolet (EM) | 3×10⁸ m/s | 770 THz – 30 PHz | Sunburn, germicidal lamps, fluorescence |
| X-rays (EM) | 3×10⁸ m/s | 30 PHz – 30 EHz | Medical imaging, airport security |
| Sound (mechanical) | 343 m/s in air | 20 Hz – 20 kHz (audible) | Speech, music, ultrasound (> 20 kHz) |
| Seismic P-waves | 5–8 km/s in rock | 0.1 – 2 Hz | Earthquakes, underground exploration |
Types of Waves: Transverse and Longitudinal
Transverse waves: The oscillation is perpendicular to the direction of energy propagation. Shaking a rope up and down sends a transverse wave horizontally along the rope. All electromagnetic waves are transverse — the electric and magnetic fields oscillate perpendicular to the direction of travel. Light can be polarized because it is transverse.
Longitudinal waves: The oscillation is parallel to the direction of energy propagation. Sound waves are longitudinal — air molecules compress and expand along the direction the sound travels. Compressions (high pressure regions) and rarefactions (low pressure regions) alternate along the wave path. P-waves (primary seismic waves) are also longitudinal.
Surface water waves are actually a combination: water particles move in approximately circular paths, which has both transverse and longitudinal components. The motion is transverse at the surface crest and longitudinal at the sides of each circular orbit.
Standing waves occur when two identical waves travel in opposite directions and superpose: interference creates fixed nodes (no displacement) and antinodes (maximum displacement). Standing waves explain resonance in musical instruments — the string or air column resonates at frequencies where standing waves fit exactly.
Key Wave Phenomena: Reflection, Refraction, Diffraction, Interference
Reflection: Waves bounce off a boundary. The angle of incidence equals the angle of reflection (law of reflection). Echoes are reflected sound waves; mirrors reflect light. When a wave reflects from a fixed boundary, the reflected wave is inverted.
Refraction: Waves change speed (and wavelength) when entering a new medium, causing a change in direction. Light bends when entering glass or water (Snell's law). Seismic waves refract through Earth's layers. Frequency does not change during refraction — only speed and wavelength change.
Diffraction: Waves spread out after passing through an opening or around an obstacle, especially when the opening is comparable in size to the wavelength. Long-wavelength radio waves diffract around buildings; short-wavelength X-rays do not diffract around everyday objects. Diffraction limits the resolution of optical instruments.
Interference: When two waves overlap, they superpose (add together). Constructive interference (waves in phase) produces larger amplitude; destructive interference (waves out of phase by half a wavelength) produces smaller amplitude or silence. Interference is responsible for thin-film colors (soap bubbles, oil slicks) and noise-cancelling headphones.