Illustration of the normal modes

• Consider a perfectly elastic string fixed at its ends.
• This physical system describes the strings of musical instruments well in the harmonic regime, but cannot account for many interesting phenomena of the anharmonic regime (see Links and further reading to find out more).

• The normal modes of the string are characterised by a single integer
• Given the size of the string, the material it is made of and its tension, the natural frequency of each mode is determined only by this number.
• It gives directly the number of antinodes that the string forms as it oscillates.

• For example, mode {2} means there are 2 antinodes and, correspondingly, 3 nodes, counting the two at the ends, which are fixed for every mode of vibration.

	corda_freq_1.mp3 mode {1}, ${\displaystyle f=f_{0}\!}$
	corda_freq_2.mp3 mode {2}, ${\displaystyle f=2f_{0}\!}$
	corda_freq_3.mp3 mode {3}, ${\displaystyle f=3f_{0}\!}$
	corda_freq_4.mp3 mode {4}, ${\displaystyle f=4f_{0}\!}$

Links and further reading

• The number indicating the mode is directly proportional to the frequency at which that mode oscillates. This means, for example, that mode 4 oscillates at twice the frequency of mode 2. This has important consequences for our musical system. See the sections on the monochord and scales and on the Pythagorean scale

• See the section questions and answers for questions and curiosities about normal modes, musical instruments and more.