Stretched string

Practice Set a ladder up on saw horses and practice crawling on it. Also, stretch string above the ladder to force you to stay low. 

Since an electron has wave character, we can describe its motion with a wave equation, as we do in classical mechanics for the motions of a water wave or a stretched string or a drum. If the system is one-dimensional, the classical wave equation is... 

To demonstrate this method, consider the geometry shown in Fig. 13-16, and let us try to find the view factor F, between surfac-es I and 2. The first thing we do is identify the endpoints of the surfaces (the points A, B, C, and /)) and connect them to each otlrer with tightly stretched strings, which are indicated by dashed lines. Hottel has shown that the view factor F, 2 c n be expressed in terms of the lengths of these stretched strings, which are straight lines, as... 

This linear homogeneous partial differential equation represents the motion of stretched strings, the small oscillations of air in narrow (organ) pipes, and the motion of waves on the sea if the water is neither too deep nor too shallow. Let us now proceed to the integration of this equation. 

Each layer of the grid will be modeled by two frames with stretched strings located perpendicularly to each other. We can then use the results from the previous section. If all drops in the oncoming flow running into the mesh bundle have the same size, then the CE of the mesh droplet catcher is... 

Frequency of vibrating strings n. The fundamental frequency of a stretched string is given by... 

The typical chain conformation in this case can be viewed as a nearly completely stretched string of blobs (so-called Pincus blobs) r Ngi, where Ng the number of blobs, bg is... 

Fig. 9.11 Although an infinite numher of solutions of the Schrodinger equation exist, not all of them are physically acceptable. Acceptable wavefunctions have to satisfy certain boundary conditions, which vary from system to system. In the example shown here, where the particle is confined between two impenetrable walls, the only acceptable wavefunctions are those that fit between the walls (like the vibrations of a stretched string). Because each wavefunction corresponds to a characteristic energy and the boundary conditions rule out many solutions, only certain energies are permissible.

The statement, which inspired the title of this chapter, is traditionally credited to Pythagoras in recognition of the fundamental discovery that the pitch produced by the stretched string on a musical instrument is numerically related to the fractional length of its vibrating part. It was repeated many centuries later in somewhat different terms by Emile de Chancourtois, codiscoverer of elemental periodicity, who claimed [1] that... 

Figure 14 The main features of the force law associated with the extension of a globular polysoap. Two coexistence regimes are involved. For weak deformations, a globule of closely packed micelles coexists with a stretched string of micelles. Stronger deformations involve coexistence of dissociated amphiphiles and weakly perturbed intrachain micelles. Eventually, all the amphiphiles are dissociated. The intrachain micelles are depicted as spheres while the dissociated amphiphiles are represented as rods. (Adapted from Ref. 63.)...

Here the first term is the radius of the globule and the second is the span of the stretched string of micelles. When nf is sufficiently large we may approximate dR as Ri evedm lp and the corresponding force law / = -dF/dR is... 

Knowing it is straightforward to obtain the brash thickness L and the free energy per chain Fcorona- L is determined by monomer conservation. Within this picture each grafted chain is a fully stretched string of blobs and the number of monomers per chain N is... 

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