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THE IB SAYS
THE IB SAYS
Essential idea: When travelling waves meet they can superpose to form standing waves in which energy may not be transferred.
Understandings: The nature of standing waves; Boundary conditions; Nodes and antinodes
Applications and skills: Describing the nature and formation of standing waves in terms of superposition; Distinguishing between standing and travelling waves; Observing, sketching and interpreting standing wave patterns in strings and pipes; Solving problems involving the frequency of a harmonic, length of the standing wave and the speed of the wave
Guidance: Students will be expected to consider the formation of standing waves from the superposition of no more than two waves; Boundary conditions for strings are: two fixed boundaries; fixed and free boundary; two free boundaries; Boundary conditions for pipes are: two closed boundaries; closed and open boundary; two open boundaries; For standing waves in air, explanations will not be required in terms of pressure nodes and pressure antinodes; The lowest frequency mode of a standing wave is known as the first harmonic; The terms fundamental and overtone will not be used in examination questions
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The definition of standing waves
The definition of standing waves
Unlike progressive waves, standing waves do not transfer energy. Instead, along the length (e.g. strings), boundary (e.g. water or plates) or volume (e.g. wind instruments) of the medium there is varying motion of the constituents of the medium. In a travelling wave all parts of the wave are oscillating with varying displacement within each phase. The maximum displacement of a travelling wave is called its amplitude. However, in a standing wave every part of the phase has a different amplitude and the each part has a maximum displacement of its own amplitude. The locations of maximum amplitude are called antinodes. The locations of zero displacement are called nodes.
The formation of standing waves
The formation of standing waves
Standing waves are formed by superposition from travelling waves. These could be external waves from different sources, but are more commonly formed by reflection. With no energy losses a standing wave could exist indefinitely, but as there are almost always energy loses most standing waves are temporary or must be externally driven.
Standing waves on surfaces
Standing waves on surfaces
If a surface, either liquid or a solid that can vibrate, is excited appropriately then standing waves can be setup in the surfaces. A classic example of this is the Chaldni plate.
Standing waves in pipes
Standing waves in pipes
Stringed instruments rely on standing waves in a string. Drums and cymbals rely on standing waves on a surface. Wind instruments rely on a standing waves being set up in a tube or pipe. Tubes or pipes can be open at both ends or only at one end. These different boundary conditions will result in different frequencies for pipes of the same length.
Resources from textbooks
Resources from textbooks
Oxford Physics: pages 158 - 162, covers all of standing waves
Hamper HL (2014): pages 178 - 180
Relevant questions from Dot Point Physics (11 Wave phenomena)
Relevant questions from Dot Point Physics (11 Wave phenomena)
pages 81-82 (to page 86 including more calculations, see next page) - NB: This used to be a HL topic so is in the HL book.
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