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The simulation diagram for the ideal string with the simplest frequency-dependent loss filter is shown in Fig. 9.1.
This is why we call them ''overtones" instead of ''harmonics". A perfectly flexible ideal string may have exactly harmonic overtones.
Another interesting interpretation of a Schroeder allpass section is as a digital waveguide model of the driving-point impedance of an ideal string (or cylindrical acoustic tube) which is reflectively terminated at a real impedance.
By starting with an "ideal" string that, when plucked, vibrates forever, Smith was able to reduce the number of computations that it takes to calculate the position of the string by a factor of 100 to 1,000, making it possible to run the simulation using current DSP chips.
Ideal strings transmit tension forces instantaneously in action-reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object.
Ideal string will be about six inches shorter than the bow itself.
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They can be combined with ideal pulleys which allow ideal strings to switch physical direction.
Tension forces can be modeled using ideal strings which are massless, frictionless, unbreakable, and unstretchable.
For the purposes of most physics problems, we assume ideal strings - in other words, that our rope, cable, etc. is thin, massless, and can't be stretched or broken.
The lower strings would have to be modeled using a non-ideal string since it has so much mass.
Figure 6.1: The ideal vibrating string.
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