Waves are disturbances that transfer energy from one place to another without transferring matter. The medium (air, water, a string) oscillates back and forth, but the wave pattern moves forward. This distinction is key: the ocean wave moves across the water, but the water molecules mostly move up and down.
Transverse waves have particle motion perpendicular to the wave's direction. Light, a wave on a plucked string, and ripples on a pond are all transverse. Longitudinal waves have particle motion parallel to the wave's direction — sound waves in air are the best example, with alternating regions of compression (high pressure) and rarefaction (low pressure).
Three properties define a wave: frequency, wavelength, and amplitude. Frequency (f) is the number of complete oscillations per second, measured in hertz (Hz). Wavelength (λ) is the distance between consecutive identical points on the wave (peak to peak, or trough to trough). Amplitude is the maximum displacement from the rest position — it determines the wave's energy and, for sound, its loudness or for light, its brightness.
The wave equation relates these quantities: v = fλ, where v is the wave speed. Sound travels at about 343 m/s in air at room temperature. Light travels at approximately 3 × 10⁸ m/s in a vacuum. When a wave enters a new medium, its speed changes — and so does either its frequency or wavelength (frequency stays constant when crossing a boundary, which is why the wavelength changes).
The electromagnetic spectrum arranges all electromagnetic waves by wavelength (or frequency). From longest wavelength to shortest: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All travel at the speed of light in a vacuum. Visible light spans only a narrow range (about 400-700 nm), from red (longest visible wavelength) to violet (shortest). Higher frequency means higher energy — which is why ultraviolet light can cause sunburn and X-rays can penetrate tissue.
Wave interference occurs when two waves overlap. Constructive interference happens when peaks align with peaks, creating a larger amplitude. Destructive interference happens when peaks align with troughs, partially or completely canceling. Noise-canceling headphones use destructive interference: a microphone detects ambient sound, and the headphones produce the opposite wave, canceling the noise.