University of St Andrews
School of Physics and Astronomy

9.  Standing Waves

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Associated tutorial questions (St Andrews only)

• Standing waves - when two oppositely directed but otherwise similar waves pass through each other, a "standing wave" is formed
• Interactive Jave Demo of formation of standing wave
• This standing wave does not appear to travel, but the particles still oscillate
• The amplitude of the standing wave varies with position - note the nodes and antinodes
• Standing waves are often produced by one wave being reflected at the end of a string or air column: the phase shift on reflection is important
• Examples of standing waves on string and in air columns
• The string or air column will support a set of allowed standing wave wavelengths - the resonant modes. 
• If we know the speed of the wave in the string or air column, we can then work out the frequency of the standing wave.  If we change the tension of a violin string, the allowed standing wave wavelengths remain the same (fixed by the boundary conditions), but as the wave-speed on the string changes, the frequency of oscillation of the string will change.
• The frequency of any radiated sound wave will be the same as that of the standing wave
• Standing optical waves are also important, for example in a laser oscillator.   There must be an integer number of half wavelengths between the mirrors, in direct analogy with a standing wave on a string.
• Standing waves are also important in quantum phenomena.

Similar material to that presented in the lectures is available at:-

• Halliday, Resnick, & Walker - Chapters on:-     Waves-I and Waves-II

Associated tutorial questions (St Andrews only)
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Created by, and copyright of, Bruce Sinclair, University of St Andrews; last modified 11/09/01