Summarizing Superposition and Interference

Summary

• Superposition is the combination of two waves at the same location.
• Constructive interference occurs when two identical waves are superimposed in phase.
• Destructive interference occurs when two identical waves are superimposed exactly out of phase.
• A standing wave is one in which two waves superimpose to produce a wave that varies in amplitude but does not propagate.
• Nodes are points of no motion in standing waves.
• An antinode is the location of maximum amplitude of a standing wave.
• Waves on a string are resonant standing waves with a fundamental frequency and can occur at higher multiples of the fundamental, called overtones or harmonics.
• Beats occur when waves of similar frequencies \({f}_{1}\) and \({f}_{2}\) are superimposed. The resulting amplitude oscillates with a beat frequency given by
  \({f}_{\text{B}}=\mid {f}_{1}-{f}_{2}\mid .\)

Glossary

antinode

the location of maximum amplitude in standing waves

beat frequency

the frequency of the amplitude fluctuations of a wave

constructive interference

when two waves arrive at the same point exactly in phase; that is, the crests of the two waves are precisely aligned, as are the troughs

destructive interference

when two identical waves arrive at the same point exactly out of phase; that is, precisely aligned crest to trough

fundamental frequency

the lowest frequency of a periodic waveform

nodes

the points where the string does not move; more generally, nodes are where the wave disturbance is zero in a standing wave

overtones

multiples of the fundamental frequency of a sound

superposition

the phenomenon that occurs when two or more waves arrive at the same point