are produced by the interference of two waves traveling in opposite directions with the same frequency and amplitude
Parts of a standing wave
nodes
locations where the amplitude is zero (or at least a minimum)
always form at fixed ends (closed ends)
antinodes
locations where the amplitude is a maximum
always form at free ends (open ends)
Resonance
is a noticeable increase in the amplitude of a wave
occurs when the driving frequency matches one of the natural frequencies of a system
Standing waves and resonance
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
if it has a wavelength that allows nodes to form at the fixed ends and antinodes to form at the free ends
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
The harmonic with the lowest frequency and longest wavelength is called the fundamental frequency (sometimes shortened to the fundamental).
Harmonics other than the fundamental are called overtones because they have frequencies higher than the fundamental (they are above or over 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
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
the overtones are odd multiples of the fundamental frequency
