IB DP Physics: SL复习笔记4.5.1 The Nature of Standing Waves

The Nature of Standing Waves

  • Standing waves are produced by the amplitude travelling in opposite directions
  • This is usually achieved when a travelling wave superimposes its reflection
    • The superposition produces a wave pattern where the crests and troughs do not move


Formation of a stationary wave on a stretched spring fixed at one end

Formation of Standing Waves

  • Standing waves are formed from the principle of superposition. This is when:

Two waves travelling in opposite directions along the same line with the same frequency superpose

  • The principle of superposition applies to all types of waves i.e. transverse and longitudinal, progressive and stationary
  • The waves must have:
    • The same wavelength
    • A similar amplitude
  • As a result of superposition, a resultant wave is produced


A graphical representation of how stationary waves are formed - the black line represents the resulting wave

Comparing Progressive and Standing Waves

  • Standing waves (or stationary waves) store energy
  • Progressive waves (or travelling waves) transfer energy
  • The table below outlines the main differences between progressive and stationary waves

Table of Differences Between Progressive and Stationary Waves


Worked Example

A travelling wave is incident on a barrier. The wave profile is shown below.


The travelling wave reflects off the barrier. The reflected and incident waves superimpose.

State whether or not a standing wave is formed.

  • For standing waves to be formed, the half-cycles of the wave profile must be symmetrical (i.e. the same but inverted)
  • For this wave, the half-cycles are not symmetrical
    • The leading edge is straight
    • The trailing edge is sinusoidal
  • When the incident and reflected waves superimpose, they will not cancel out at any point
  • Therefore a standing wave is not formed