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
