AQA A Level Physics复习笔记3.2.2 Formation of Stationary Waves

Formation of Stationary Waves

 

The Principle of Superposition

  • The principle of superposition states:

When two or more waves with the same frequency arrive at a point, the resultant displacement is the sum of the displacements of each wave

  • This principle describes how waves that meet at a point in space interact
  • When two waves with the same frequency and amplitude arrive at a point, they superpose either:
    • In phase, causing constructive interference. The peaks and troughs line up on both waves and the resultant wave has double the amplitude
    • In anti-phase, causing destructive interference. The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude

     

 

8.1.1-Constructive-and-destructive

Waves in superposition can undergo constructive or destructive interference

 

 

  • The principle of superposition applies to all types of waves i.e. transverse and longitudinal, progressive and stationary

The Formation of Stationary Waves

  • A stationary wave is formed when:

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

  • The waves must have:
    • The same wavelength)
    • A similar amplitude

     

  • As a result of superposition, a resultant wave is produced

3.2.2-Formation-of-stationary-waves_1

Nodes and antinodes are a result of destructive and constructive interference respectively

 

  • At the nodes:
    • The waves are in anti-phase meaning destructive interference occurs
    • This causes the two waves to cancel each other out

     

  • At the antinodes:
    • The waves are in phase meaning constructive interference occurs
    • This causes the waves to add together

     

  • Each point on the stationary wave has a different amplitude (unlike a progressive / travelling wave where each point has the same amplitude)

 

3.2.2-Superposition-of-stationary-waves

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

 

Examples of Stationary Waves

Stretched Strings

  • Vibrations caused by stationary waves on a stretched string produce sound
    • This is how stringed instruments, such as guitars or violins, work

     

  • This can be demonstrated by a length of string under tension fixed at one end and vibrations made by an oscillator:

8.1.2-Stationary-wave-string

Stationary wave on a stretched string

 

  • At specific frequencies, known as resonant frequencies, a whole number of half wavelengths will fit on the length of the string
  • As the resonant frequencies of the oscillator are achieved, standing waves with different numbers of minima (nodes) and maxima (antinodes) form

Microwaves

  • A microwave source is placed in line with a reflecting plate and a small detector between the two
  • The reflector can be moved to and from the source to vary the stationary wave pattern formed
  • By moving the detector, it can pick up the minima (nodes) and maxima (antinodes) of the stationary wave pattern

 

8.1.2-Stationary-wave-microwave

Using microwaves to demonstrate stationary waves

 

Sound Waves

  • Sound waves can be produced as a result of the formation of stationary waves inside an air column
    • This is how musical instruments, such as clarinets and organs, work

     

  • This can be demonstrated by placing a fine powder inside the air column and a loudspeaker at the open end
  • At certain frequencies, the powder forms evenly spaced heaps along the tube, showing where there is zero disturbance as a result of the nodes of the stationary wave

8.1.2-Air-column-stationary-waves

Stationary wave in an air column

 

  • In order to produce a stationary wave, there must be a minima (node) at one end and a maxima (antinode) at the end with the loudspeaker

Exam Tip

Always refer back to the experiment or scenario in an exam question e.g. the wave produced by a loudspeaker reflects at the end of a tube. This reflected wave, with the same frequency, overlaps the initial wave to create a stationary wave.

 

转载自savemyexams

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