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Transverse Standing Waves
Introduction
A mechanical wave is the propagation through a medium of a disturbance of the
medium. Consider the string under tension shown below. In this case, the string
itself is the medium that carries the wave.
Sketch
A continuous disturbance of the stretched string by the oscillator creates a train of
transverse waves that travels along the string. The waves are reflected at the pulley.
The leftward traveling reflected waves interfere with the rightward traveling incident
waves. The result under certain conditions is a standing wave pattern along the
length of the string.
The system resonates when the frequency of the oscillator matches a natural
frequency of the string under tension. Natural frequencies, in this case, are those
wave frequencies for which an integer number of half-wavelengths (segments) fit
along the string (which is "fixed" at both ends). Resonance corresponds to the
appearance of standing wave patterns.
