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  1. space. The typical example is the vibrating string. When one plucks a violin, or guitar, string, the string vibrates ex-hibiting a variety of sounds. These are enhanced by the violin case, but we will only focus on the simpler vibrations of the string. We will consider the one dimensional wave motion in the string. Physically,

  2. Transverse vibration of a taut string Referring to Figure 1, consider a taut string stretched between two fixed points at x =0 and x = L. Let the cross-sectional area be S. If there is an initial stretching of ∆L,the initial tension T must be ∆L T = ES L by Hooke’s law, where E is Young’s modulus.

  3. Vibrating strings. Really need at least three coupled 1D waveguides: ∗ Horizontally polarized transverse waves ∗ Vertical polarized transverse waves ∗ Longitudinal waves (Typically 1 or 2 WG per string used in practice) Bowed strings also require torsional waves (Typical: one waveguide per string [plane of the bow])

  4. Lab 11.Vibrating Strings GoalsTo experimentally determine the relationships between the fundamental resonant frequency of a vibrating string and its length, its mass per unit length, and the tension in the string. •To introduce a useful graphical method for testing whether the quantities x and y are related

  5. Lab 12.Vibrating Strings GoalsTo experimentally determine the relationships between the fundamental resonant frequency of a vibrating string and its length, its mass per unit length, and the tension in the string. •To introduce a useful graphical method for testing whether the quantities x and y are related

  6. two categories: the nature of how string is excited, and small corrections or additions to the wave equation. The wave equation (1) can be readily derived from Newton's second law. The parameter c is equal to .JTJ JL, where T is the tension and JL mass per unit length of the string.

  7. A particular quantum vibration mode of the closed string describes a graviton, the quantum of the gravitational field. A particular quantum vibration of an open string describes a photon, the quantum of the electromagnetic field. It is the magic of quan-tization that makes these results possible.

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