Hertz, defined

Although Newton had measured the black spot at the contact of glass spheres, and also seen the black spot expand and contract reversibly as the spheres were pressed together, he did not pursue the relationship between the spot size and load. Almost 200 years were to elapse before Hertz defined the connection published in 1882. Hertz was a 23-year-old assistant to Helmholtz in Berlin when he was stimulated by Newton s rings and derived the elastic theory of sphere contact in his Christmas vacation in 1880." He found that the spot diameter increased with the cube root of load F, showed that the elastic modulus E, Poisson s ratio v and sphere diameter D were also important, and verified his equation... 

Frequency, /, is defined as the number of repetitions of a specific forcing function or vibration component over a specific unit of time. It is the inverse of the period, l/r, of the vibration and can be expressed in units of cycles per second (cps) or Hertz (Hz). For rotating machinery, the frequency is often expressed in vibrations per minute (vpm). 

Fourier transform mass spectrometry is made possible by the measurement of an AC current produced from the movement of ions within a magnetic field under ultra-high vacuum, commonly referred to as ion cyclotron motion.21 Ion motion, or the frequency of each ion, is recorded to the precision of one thousandth of a Hertz and may last for several seconds, depending on the vacuum conditions. Waveform motion recorded by the mass analyzer is subjected to a Fourier transform to extract ion frequencies that yield the corresponding mass to charge ratios. To a first approximation, motion of a single ion in a magnetic field can be defined by the equation... 

NMR spectra were recorded on Bruker AC200 spectrometers unless indicated otherwise deuteriated chloroform was used as solvent and tetramethylsi-lane as internal reference. Chemical shifts (8) are given in ppm. The following abbreviations were used to define the multiplicities s, singlet d, doublet t, triplet q, quartet m, multiplet br, broad coupling constants (/) are measured in Hertz (Hz). IR spectra were recorded on a Nicolet Magna-550 FTIR... 

E. Winkler, F. Grashof, H. Hertz,8 etc., have studied the stresses which are set up when two elastic isotropic bodies are in contact over a portion of their surface, when the surfaces of contact are perfectly smooth, and when the press, exerted between the surfaces is normal to the plane of contact. H. Hertz showed that there is a definite point in such a surface representing the hardness defined as the strength of a body relative to the kind of deformation which corresponds to contact with a circular surface of press. and that the hardness of a body may be measured by the normal press, per unit area which must act at the centre of a circular surface of press, in order that in some point of the body the stress may first reach the limit consistent with perfect elasticity. If H be the hardness of a body in contact with another body of a greater hardness than H, then for a circular surface of pressure of diameter d press. p radius of curvature of the line p and the modulus of penetration E,... 

Greek letter nu), of the radiation. The unit of frequency, 1 hertz (1 Hz), is defined as 1 cycle per second ... 

Similar to the Hillion-Quinnez model, Rodrigues and Vaz defined an EM field that is a function of a specific Hertz potential ... 

In essence, the chemical shift of a nucleus such as proton ( I I) is its resonance frequency. It is usually expressed in parts per million (ppm) relative to a standard. The most common standard is tetramethylsilane [(CH3)4Si, TMS] which defines 0 on the delta (8) scale and 10 on the older, less used t scale. A small amount of TMS is typically added to the NMR solution to be examined. The presence of an internal standard minimizes experimental variations. This is particularly important because the chemical shift is typically a change of only a few hertz per megahertz, hence the part per million (ppm) scale. The separation of peaks will be greater in hertz at higher field but spectra obtained at different field strengths are comparable on the ppm scale. Common reference standards are listed in Table 6.32. 

The most important modem system of units is the SI system, which is based around seven primary units time (second, abbreviated s), length (meter, m), temperature (Kelvin, K), mass (kilogram, kg), amount of substance (mole, mol), current (Amperes, A) and luminous intensity (candela, cd). The candela is mainly important for characterizing radiation sources such as light bulbs. Physical artifacts such as the platinum-iridium bar mentioned above no longer define most of the primary units. Instead, most of the definitions rely on fundamental physical properties, which are more readily reproduced. For example, the second is defined in terms of the frequency of microwave radiation that causes atoms of the isotope cesium-133 to absorb energy. This frequency is defined to be 9,192,631,770 cycles per second (Hertz) —in other words, an instrument which counts 9,192,631,770 cycles of this wave will have measured exactly one second. Commercially available cesium clocks use this principle, and are accurate to a few parts in 1014. 

We will summarize the two electrical properties which define the electrical characteristics, namely, the dielectric constant relative to free space e and the conductivity a. Both properties change with temperature and strongly with frequency. As a matter of fact, as the frequency increases from a few Hertz to gigahertz, the dielectric constant decreases from several million to only a few units. Concurrently, the conductivity increases from a few mMho/cm to nearly a thousand. 

The candela (cd) is the SI unit of luminous intensity, defined as follows In a given direction, 1 candela of a source emits monochromatic radiation of frequency v = 540 x 1012 hertz and has a radiant intensity in that direction of... 

At this point we can be more explicit about what we mean by NMR time scale. We will define the dimensionless exchange ratio (R) as the total rate constant (k, in reciprocal seconds) divided by the difference in frequency between two exchanging signals (Av0, in hertz) ... 

In this equation A is the wavelength in meters, v is the frequency in cycles per second, and c is the speed of light, a defined quantity with the exact value of 2.99792458 X 108 m/s. In the SI system, cycles is understood, and the unit cycles per second becomes 1/s, or s-1, which is called the hertz (abbreviated Hz). 

Takahashi s approach is diametrically opposed to Hertz s electrostatic model in that it assumes the source of the transient electric field gradients to arise from symmetry distortions in the first solvation shell. Moreover, the theory is of less general applicability since it requires a well defined solvation complex hence confining it to strongly hydrating cations. 

The experimental foundation of the quantum theory of atomic structure as put forward by Bohr, lies in the stability of the atom and in the existence of discrete energy levels and the ability of the atom to absorb and emit energy only in quanta, as demonstrated by the discontinuous nature of atomic spectra and by the critical potential measurements of Franck and Hertz. Bohr postulated that the atom could only exist in a limited number of orbits or stationary states, which were defined by the quantum condition that the angular momentum can assume only certain limited values which are given by the expressioiT ... 

The wavelength, in units of cm or pm, is defined as the distance between peaks or troughs of the wave. The frequency of the wave is the number of peaks passing a fixed point per unit of time. The unit of frequency is the Hertz, i.e., the cycles or waves per second. 

Baer et al (1961) later considered the indentation process in which large loads are placed on a spherical penetrator and the material beneath the indenter becomes permanently displaced. In addition, he defined the recovery process which occurs immediately after the load is released analysing it in terms of the elastic concepts developed by Hertz (Love, 1927). 

Other terms used extensively in spectroscopy are the wavenumber and the frequency. The wavenumber is defined as the number of waves per unit of length (usually quoted in units of reciprocal centimetres (cm4 where 1 cm = 10 2 m) and is the reciprocal of the wavelength in centimetres, i.e. HX. The use of wavenumber is usually confined to infrared spectroscopy The frequency is defined as the number of waves emitted from a source per second the unit of frequency is the hertz (Hz 1 Hz = 1 wave per second), and the symbol for it is v (the Greek letter nu ). 

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