A wave is a disturbance that transfers energy through a medium without transporting matter. The key properties that define any wave are amplitude, wavelength, frequency, and period. Amplitude represents the maximum displacement from equilibrium. Wavelength is the distance between consecutive peaks. Frequency measures how many complete waves pass a point per second, while period is the time for one complete cycle. These properties are mathematically related through the wave equation.
Waves can be classified in two main ways. First, by their medium requirement: mechanical waves need a physical medium to travel through, like sound waves in air or water waves on a surface. Electromagnetic waves, such as light and radio waves, can travel through vacuum. Second, by particle motion direction: transverse waves have particles moving perpendicular to the wave direction, like water waves. Longitudinal waves have particles moving parallel to wave propagation, creating compressions and rarefactions, as seen in sound waves.
The fundamental wave equation y equals A sine of kx minus omega t plus phi mathematically describes all wave motion. Each parameter has physical meaning: A is the amplitude representing maximum displacement, k is the wave number related to wavelength, omega is angular frequency related to how fast the wave oscillates, and phi is the phase constant determining the initial position. The wave speed v equals f lambda, which also equals omega over k, connecting frequency and wavelength through the wave equation parameters.
Wave interference occurs when two or more waves meet and combine according to the superposition principle. The resultant wave is simply the sum of the individual waves at each point. Constructive interference happens when waves are in phase, adding their amplitudes together. Destructive interference occurs when waves are out of phase, potentially canceling each other out. Standing waves form when two waves of equal frequency and amplitude travel in opposite directions, creating stationary patterns with nodes where amplitude is always zero and antinodes where amplitude is maximum. These phenomena are fundamental to musical instruments and many wave applications.
When waves encounter boundaries between different media, they undergo reflection and transmission. At a fixed boundary, the reflected wave experiences a phase inversion, appearing upside down. At a free boundary, reflection occurs without phase change. The transmitted wave continues into the new medium, often with different amplitude and wavelength due to the change in wave speed. The reflection and transmission coefficients must sum to one, conserving energy. Wave impedance, which depends on the medium properties, determines the exact ratios of reflected and transmitted energy.