Struck string

Fig. 2 Suing with fixed ends (a) the plucked string (b) the struck string.

Chaigne and Askenfelt, 1994] Chaigne, A. and Askenfelt, A. (1994). Numerical Simulations of Piano Strings. I. A Physical Model for a Struck String Using Finite Difference Methods. J. Acoustical Soc. of America, 95(2) 1112-1118. 

Chapter 9 looks at one of the most fundamental physical vibration systems, the plucked/struck string. We develop an increasingly more realistic, yet still computationally efficient, series of models of plucked and bowed string instruments. Appendix B has derivations and proofs related to the plucked string. 

Dennis s rap drew on the theory of sound. If you pluck a string, it will sound in the octave in which it is struck, but it will also sound in octaves above and below its key. It has what are called harmonic overtones. If you strike the chord and then squelch it, you can still hear the harmonic overtones, a phenomenon that had fascinated Pythagoras. Dennis pointed out to us that one can use two sounds to cancel each other if the two sounds are exactly the same in relation to each other. 

Special function keys, such as those in some word processing systems are a hybrid of both of the above. The keys can either represent commands or a form of interactive menu depending on your point of view. In some of the Hewlett-Packard terminals the split between functions is clearer. Keys located under the face of the screen can be used for menu selection, while others can be programmed to enter preset commands (when a key is struck, it causes a user defined character string to be sent to the system). 

When a string in a musical instrument is struck or bowed, it will usually not vibrate according to a single harmonic. The following Fourier series is a linear... 

The best way to visualise the functioning of this technique is to imagine what happens when the string of a monochord is struck at a specific point two waves travel in opposite directions and when they reach a bridge, some of their energy is absorbed and some is reflected back to the point of impact, causing resonance and interference (Figure 4.7). 

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