Waves within Boundaries : Strings

A guitar string is fixed at both ends. If we pluck a guitar string in the middle, near the twelfth fret, the string oscillates with SHM. The tension and mass per unit length defines how fast the string moves in both directions down the string to either end, where it reflects with a phase change of π radians, superposing with the wave coming the other way. This sets up a resonant condition in the string, each part of the string oscillating in phase with variable amplitude down its length, maximum amplitude being in the middle. The string length defines the fundamental frequency ( v = fλ) and is half a wavelength . Plucking the first harmonic on the twelfth fret sets up a standing wave an octave higher, with a NODE or position of no disturbance in the middle and antinodes on either side.

The fundamental, and first to fourth harmonics are shown.

 

Nodes (x=0) are at each end
Nodes (x=0) are at each end
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