Incident Wave (入射波)
Reflected Wave (反射波)
Standing Wave (驻波)
Nodes & Antinodes
Wave Parameters
String Parameters
Wave Properties
Display Options
Harmonics and Resonance
Wave Equations
What is a Standing Wave?
A standing wave is a wave that remains in a constant position, created by the interference of two waves traveling in opposite directions with the same frequency and amplitude. This phenomenon occurs when a wave is reflected at a boundary, such as a string fixed at both ends, an air column in a musical instrument, or electromagnetic waves in a cavity.
Nodes and Antinodes
Nodes are points of zero amplitude that remain stationary. They occur where the incident and reflected waves always cancel each other out (destructive interference). For a standing wave on a string fixed at both ends, nodes occur at positions x = nλ/2, where n is an integer. Antinodes are points of maximum amplitude where constructive interference is maximum, occurring at x = (2n+1)λ/4.
Harmonics and Resonance
Standing waves form at specific resonant frequencies called harmonics. The fundamental frequency (first harmonic) has one antinode in the center. Higher harmonics (2nd, 3rd, 4th, etc.) have increasing numbers of nodes and antinodes. The frequency of the nth harmonic is n times the fundamental frequency: f_n = n × f₁. This principle is fundamental to musical instruments, where different harmonics create different pitches and timbres.
Applications
Standing waves have numerous practical applications: musical instruments (guitar strings, wind instruments, organ pipes) rely on standing wave patterns to produce specific notes; optical cavities use standing electromagnetic waves in lasers; microwave ovens use standing electromagnetic waves for heating; quantum mechanics describes electrons in atoms as standing matter waves (orbitals); and architectural acoustics considers standing wave patterns for concert hall design.