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Wave Equation. Waves in Strings. Sound

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Book Id: WPLBN0000686534
Format Type: PDF eBook
File Size: 590.95 KB.
Reproduction Date: 2005
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Title: Wave Equation. Waves in Strings. Sound  
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Language: English
Subject: Science., Physics, Physics--Research
Collections: Physics Literature
Historic
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Wave Equation. Waves in Strings. Sound. (n.d.). Wave Equation. Waves in Strings. Sound. Retrieved from http://www.worldebooklibrary.org/


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Physics Literature

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Introduction: The method we developed in the previous chapter makes it possible to study the vibrations of any real system. Let us discuss for example a guitar?s string. We can consider the string as a chain of masses. The masses of the chain correspond to the atoms in the string. Because there are zillions of atoms in a string, there is a correspondingly huge number of normal modes. However, the modes we excite when we play the guitar are a few modes for which the wavelength is of the order of the size of the guitar, say 1m. This must be contrasted with the separation between atoms, which is of the order of 1, or 10-10 m. If you look at the normal mode solutions with long wavelengths in systems with very large N you notice that nearby masses tend to have similar displacements. In the case of the string, with the enormous discrepancy between atomic separations and music-like wavelengths, it is apparent that a huge number of atoms near a certain point x in the string are undergoing virtually identical displacements. We can thus make a continuum approximation. Rather than labeling the atoms one by one, we assume that there is a function x(x,t) that gives the displacement of the atoms near position x at time t. Since the atoms are so closely spaced compared with the wavelength of the music-like normal modes, we can assume that the function x(x,t) is continuous and differentiable. This leads to the famous wave equation.

 

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