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Standing Waves
Summary
- Traveling waves …
- Standing waves …
- do not appear to propagate
- are produced by the interference of two waves traveling in opposite
directions with the same frequency and amplitude
- Positions on a standing wave:
- node: a point where the amplitude is
zero or a minimum
(always form at fixed ends)
- antinode: a point where the amplitude
is a maximum
(always form at free ends)
- Resonance
- Resonance is the dramatic increase in amplitude of a periodic system
that occurs when the driving frequency
applied equals the natural frequency
of the system
- Standing waves form during resonance (but resonance does not always
lead to the formation of standing waves)
- A wave moving in a medium of finite length, can interfere with its own
reflection to produce a standing wave if it has the same frequency as
one of the natural frequencies of the medium
- Harmonics
- are the set of all possible standing waves in a system
- are countably infinite in number (form a countable infinite set in the
manner of whole numbers)
- Groups of harmonics:
- fundamental: harmonic with the lowest
frequency and longest wavelength
- overtones: harmonics other than the
fundamental
- When standing waves form in a linear medium that has …
- two fixed ends or two free ends …
- a whole number of half wavelengths fit inside the medium and
- the overtones are whole number multiples of the fundamental frequency.
- one fixed end and one free end …
- an odd number of quarter wavelengths fit inside the medium and
- the overtones are odd multiples of the fundamental frequency.
- Higher-dimensional cases
- You probably don't need to worry about it.
