Sixth Harmonics Research Articles

Optoacoustic spectroscopy of liquids

We report a pulsed-dye-laser optoacoustic spectroscopy technique for sensitive measurements of weak absorption spectra of liquids. We have used this technique to measure the weak visible absorption band of benzene near 607 nm, due to the sixth harmonic of the C-H stretch. We obtain a signal-to-noise ratio exceeding 102 at the absorption peak. We estimate that with improved data handling, absorption features as small as 10−7 cm−1 should be detectable in liquids. This opens up new possibilities of trace-constituent detection and pollution monitoring in the liquid phase.

Beam buncher for heavy ions

An ion beam buncher has been developed for efficient pulsing of heavy ions into a tandem accelerator. The buncher consists of a single acceleration gap, with aligned grids, which is excited by an rf voltage with a sawtooth waveform. The sawtooth is generated by combining an rf sine wave with its first three higher harmonics. The amplitudes of the second, fourth and sixth harmonics induced by the pulsed beam in a resonant cavity provide an immediate indication of the pulse width. Time-of-flight measurements yielded pulses 0.6 and 0.9 ns wide (fwhm) for 1H and 12C beams, respectively, with over 75% of the dc beam compressed into the pulses.

Physical properties of treble recorder tones suitable for baroque music

Using real and synthesized tones, we have investigated how the quality of treble recorder tones depends on their physical properties, such as harmonic structure, nonperiodic amplitude and frequency fluctuations of overtones, and noise content. By the use of a paired comparison method, the quality of the tones was judged by professional recorder players and by amateurs with some musical training. As the result, psychological interval scales of quality were constructed against (1) two parameters of harmonic structure, (2) magnitude and frequency structure of harmonic's amplitude fluctuation and (3) those of harmonic's frequency fluctuations. The best quantities are as follows: (1) Decay rate of harmonic amplitude is 4 dB/harmonic. (2) The second, fourth and sixth harmonics are some 10 dB weaker than the values calculated from this decay rate. (3) Frequency fluctuation magnitude of the second and third harmonics is about 1.7% expressed in effective value. Frequency fluctuation of the higher harmonics is rather harmful for quality.

Generation of vacuum-ultraviolet radiation by non-linear mixing processes in atoms

The authors report the experimental observation of cascade-generated sixth and tenth harmonics of Nd3+:glass laser radiation. The fifth-order non-linear susceptibility in a mixture of Na and Ar is measured and found to be chi eff(5) approximately=6*10-47 esu. Nonlinear mixing processes are used to yield 151.4, 132.5 and 117.7 nm radiation in phase-matched Cd vapour.

Electronics for the Longitudinal Active Damping System for the CERN PS Booster

Precisely tracking band-pass filters centred at the sixth and seventh harmonic of the revolution frequency are required1). During the accelerating cycle of 0.6 sec the frequency changes by a factor 2.7. The resulting tracking problem is solved by active two-path filters, where the centre frequency is governed by the frequency of a pair of sinusoidal signals in quadrature, which are generated from the accelerating RF frequency (fifth harmonic) by means of a phase-locked loop and a loop-controlled phase shifter. The phase change caused by the large frequency sweep (6 or 7 MHz) in conjunction with the delay in the feedback loop (cables, etc.) is compensated by a digital system, which computes the required phase advance from the value of the RF frequency and controls digitally the phase shift of the two-path filters. A low-frequency quadrature VCO is made to track the synchrotron frequency or harmonics hereof from analogue information about bending magnet field (momentum) and RF voltage. This quadrature pair ensures tracking of single sideband filters which permit each individual mode sideband to be examined throughout the cycle. A drive system can, by means of a similar VCO, generate any desired mode sideband, and thus excite any given mode.

Comparison of Methods for Sensitivity Determination of Point-Contact Diodes at Submillimeter Wavelength

Three independent methods were used: 1) mixing of two HCN lasers; 2) mixing of the sixth harmonic of a klystron with an HCN laser; and 3) the incremental-loss method. The results are given. The most sensitive configuration was obtained using a corner reflector. The influence of local-oscillator (LO) power on the conversion losses of the diodes are investigated.

Aural difference tone masking in normal and hearing-impaired subjects

A remote-masking paradigm was employed to assess the ability of the cochlea to generate aural difference tones in four normal-hearing subjects, two “clinically-normal” subjects, and 17 subjects with sensorineural losses of various etiologies. The hearing-impaired subjects had one of three different patterns of hearing loss. Stimuli were three, A. M. complexes composed of the fourth, fifth, and sixth harmonics of three different fundamentals. All hearing-impaired subjects had abnormal masking patterns at one or both masker levels regardless of complex or modulation depth. Moreover. the individual differences in processing ability (masking) were not predicted by pure-tone thresholds. These results demonstrated that identification of cochlear site of lesion, in and of itself, does not permit accurate inferences about cochlear processing ability. [Work supported by NIH.]

Fourier Analysis of Zooecial Shapes in Fossil Tubular Bryozoans

Fourier harmonic amplitudes provide exact characterization of the cross-sectional morphology of fossil tubular bryozoans. The Fourier method resolves a complex zooecial shape into multiple shape components (harmonics), which can be treated as individual morphologic variables. Shape elongation caused by varying zooecial orientation affects only the value of the second harmonic. Fourier harmonic coefficients reveal small changes in model shapes involving different numbers of neighboring zooecia, thickening of zooecial walls, and acanthopore variation. The number (between three and six) of neighboring zooecia controls the gross zooecial shape, as reflected in the third to the sixth harmonic. The sixth harmonic reflects the closest packing of zooecia within a colony, and its mean correlates with the colonial growth form and number of mesopores. Monticules represent the budding centers of a colony: zooecial chambers decrease in maximum diameter and become more densely packed away from the monticules. Ontogenetic changes, from the budding of new zooids to the closest packing of mature individuals, involve variation in gross zooecial form, revealed in the amplitudes of the second to the sixth harmonic. Harmonics above the sixth reflect small-scale sculpturing of the zooecial margin. The mean harmonics of different taxa suggest that Fourier values can be used for multivariate phenetic differentiation. The mean spectra of different growth forms indicate that variation in the second and sixth harmonics results from ontogenetic differences and nonmutational response to external stresses. Comparison of intrageneric variability and intracolonial variability shows that the second and sixth harmonics vary more widely among genetically identical individuals than among evolving taxa, even though the morphologies they reflect have been used as major bio-characters in bryozoan systematics. The higher numbered harmonics, especially the seventh, carry evolutionary information.

Genetic Meaning of Zooecial Chamber Shapes in Fossil Bryozoans: Fourier Analysis

Fourier harmonic amplitudes quantitatively characterize chamber shapes of fossil tubular bryozoans. The odd-numbered harmonics, particularly the seventh, carry evolutionary information. The phenotypically plastic second and sixth harmonics measure zooecial orientation and packing, respectively. As a measure of crowding, the sixth harmonic reflects mechanistic growth response to paleoenvironmental conditions.

Simplified Dynamic Simulation of HVDC System by Digital Computer Part I - Computer Program

The paper presents a dynamic simulation of an HVDC system by digital computer employing converter equations based on averaged values. The converters are represented by perfect dc generators and motors, their outputs are equal to those from real converters with the sixth and higher harmonics being neglected. The converter control circuit of the system is represented by actual hardware. Due to the simplified representation the program enables a considerable saving of computation time with minimal loss of accuracy.

Nonlinear distortion in common-emitter transistor amplifiers operated in the normal domain

Three nonlinear-distortion sources are analysed separately for polarity and magnitude of harmonics. If magnitudes are small, the resultant harmonic from these sources is the vector sum of its separated magnitudes. Universal charts are computed, to design amplifier circuits with simultaneous zero second and third harmonics. Experiments on an OC44 confirmed the theory, giving 2.5 mW with second to sixth harmonics better than -75 dB, power gain 40 dB, and no feedback or push-pull.

The Earth's Gravitational Potential, deduced from the Orbits of Artificial Satellites

Summary The numerical values of several of the higher harmonics in the Earth's gravitational potential have been obtained from the perturbations to the orbits of satellites. This paper describes the relevant methods, cursorily reviews previous results, and gives details of a fresh determination of the second, fourth and sixth harmonics from the orbits of Sputnik 2, Vanguard I and Explorer 7.

Determination of the earth's gravitational potential from satellite orbits

From the motions of the orbital planes of four satellites, values for the second, fourth and sixth harmonics in the earth's gravitational potential have been obtained. Allowance is made for atmospheric, lunar and solar perturbations and the results are compared with those of other authors.

Evaluation of the Second, Fourth and Sixth Harmonics in the Earth's Gravitational Potential

IN an article1 in Nature in 1958, it was explained how the rate of rotation of the orbital plane of an Earth satellite (the rate of regression of the nodes) could be used to evaluate the even harmonics in the Earth's gravitational potential U. At an exterior point distant r from the Earth's centre and having co-latitude θ, U may be expressed in terms of Legendre polynomials P n as : where G is the gravitational constant, M the mass of the Earth, R its equatorial radius, and the J n are constants to be determined. J 1 is zero if the equator is chosen to pass through the Earth's centre of mass. The motion of a satellite in the gravitational field specified by equation (1) has been investigated theoretically2–4, and the rate of rotation of the orbital plane, Ω, may in principle be expressed in the form : where the F n and F mn are functions of the orbital elements. Since J 2 is of order 10−3, the J n are of order 10−6 when n > 2, and the F n are of the same order as the F mn, only the J 2 2 term in the second series in equation (2) need be considered, and even in that term an approximate value of J 2 is adequate. Thus each observed value of Ω provides one linear relation between the J n, and observed values from k satellites provide k simultaneous equations between the J n. These equations are not ill-conditioned if the k orbits differ widely enough. It happens that the odd-numbered J n have little effect on Ω, and the available values5 for J 3 and J 5, namely : can be substituted into equation (2) without introducing significant error. Thus k satellites with widely different orbits—and, in particular, with widely differing orbital inclinations—will yield values of J 2, J 4, … J 2k if we are prepared to assume that the contributions of J 7, J 9 … and of J 2k + 2, J 2k + 4, … are negligible.

Gravity formulas utilizing correlation with elevation

Solutions for the first two terms of the standard gravity formula γ6(1 + β sin2 Φ) were made, all based on the assumption that the gravity anomalies in areas without observations will average the same as observed values of the same elevation. The solution by the method considered theoretically best yieldsequation imageandequation imageThe coefficients of the fourth and sixth degree zonal harmonics were also computed and used to estimate how much a flattening found from satellite motion would differ. For example, it is estimated that an orbit approximating that of 1958β would give f = 1/298.00.

The Motion of a Satellite in an Axi-symmetric Gravitational Field

Summary The equations for the variation of the osculating elements of a satellite are integrated to yield the complete perturbations of the first order due to the second harmonic, together with the secular perturbations of the second order due to the second harmonic and of the first order due to the third to sixth harmonics. A set of smoothed elements is then derived, in which the perturbations of the even harmonics have no singularities, the semi-major axis and eccentricity have no variation due to the second harmonic and the other elements have the smallest possible amplitudes of oscillation. The formulae presented will be extremely useful in the reduction of earth-satellite observations and geopotential studies based on these.

Maxima of potential gradient at Apia

The average values of potential gradient of the atmosphere between successive hourly periods 0h–1h, 1h–2h, 23h–24h, on complete days free from negative potential during the period 1924–34 have been tabulated and the means of these average values for each year are given in Table 1. The departures of the hourly means from the daily mean have been plotted to give the curve (full line) in Figure 1, the departure for 0h–1h having been plotted as the ordinate at 1h and so on.The harmonic analysis for this period of eleven years, using 24 ordinates and taking the mean average value for the period 23h–24h as the midnight value givesdV/dh = 115.3 + 15.8 sin (280° + 15t) + 33.6 sin (183° + 30t)+ 6.5 sin (30° + 45t) + 18.2 sin (295° + 60t) + 4.2 sin (146° + 75t)+ 9.1 sin (50° + 90t) where local midnight (zone time, that is, 165° west meridian time at Apia) is the epoch. Figure 1 also shows the curve (dotted line) for the above harmonic series omitting the first (constant) term. The fifth and sixth harmonics have been included because it was found that they decidedly improve the shape of the harmonic curve. The phase‐angle of the 24‐hour wave referred to midnight G. M. T. is 115° (280° zone time) and this agrees very well with the mean phase‐angle of 113° G. M. T. obtained at Mount Stromlo, Australia; but, as C. W. Allen1 points out, this represents a considerable retardation if compared with the 24‐hour wave of the world gradient, the phase‐angle of which is about 183° G. M. T. The maximum of the 24‐hour component at Apia is at 11h.3 zone time (22h.3 G. M. T.), whereas the actual maximum of potential gradient occurs between 8h and 9h (19h and 20h G. M. T.) in the morning and a secondary maximum occurs between 20h and 21h (7h and 8h G. M. T.) in the evening. From the analysis it is seen that the times of the maxima are determined mainly by the 12‐hour and 6‐hour terms, both of which have greater amplitudes than the first harmonic and hence the diurnal‐variation curve shows little resemblance to a single sine‐oscillation. In fact, under normal conditions the potential gradient in Samoa shows a strong 12‐hourly variation in the form of these two well defined maxima, the morning maximum usually being of higher potential and more protracted than the evening maximum.