The Nature of Standing Waves (DP IB Physics: SL)

• 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

• 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