# 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