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Vibration, standing waves in a string. The fundamental and the first 5 overtones in the harmonic series. A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical tone.
For example, the string might be tied at x = L to a ring that can slide freely up and down a pole. The string again has small damping and is driven by a small driving force at x = 0 . In this case, Equation ( 1 ) still describes the standing wave pattern that can form on the string, and the string has the same boundary condition of y = 0 at x = 0 .
A standing wave. The red dots are the wave nodes. A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the ...
The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality.
An example, from Mason's A History of the Sciences, [4] illustrates multi-mode vibration via a piece of string. As a natural vibrator, the string will oscillate with specific modes (the standing waves of a string in harmonic resonance), dependent on the length of the string. In classical physics, a radiator of energy will act as a natural vibrator.
Optical modulators with a high-Q microring are reported to yield outstandingly small power of modulation at a speed of > 50 Gbit/s at cost of a tuning power to match wavelength of the light source. A ring modulator placed in a Fabry-Perot laser cavity was reported to eliminate the tuning power by automatic matching of the laser wavelength with ...