The number (i) expressing the ratio of the two amplitudes is a function of the following quantities: - (T) the volume of the disturbing particle; (r) the distance of the point under consideration from it; (A) the wave-length; (b) the velocity of propagation of light; (D) and (D') the original and altered densities: of which the first three depend only upon space, the fourth on space and time, while the fifth and sixth introduce the consideration of mass.
If this be overlooked, a wrong impression may be derived as to the absolute amplitudes of the changes.
Are the amplitudes of the component harmonic waves of periods 24, 12, 8 and 6 hours; al, a2, a 3, a 4, are the corresponding phase angles.
The third line gives the range of the regular diurnal inequality, the next four lines the amplitudes of the first four Fourier waves into which the regular diurnal inequality has been analysed.
These mean values, ranges and amplitudes are all measured in volts per metre (in the open).
In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season.
- Fourier Series Amplitudes and Phase Angles.
He showed that in a simple Marconi antenna the variations of potential are a maximum at the insulated top and a minimum at the base, whilst the current amplitudes are a maximum at the top earthed end and zero at the top end.
The wave motion due to any element of the surface is called a secondary wave, and in estimating the total effect regard must be paid to the phases as well as the amplitudes of the components.
If the amplitudes a, b, c. and the epochs e, f, g....
Now we can see that two notes of the same pitch, but of different quality, or different form of displacement curve, will, when thus analysed, break up into a series having the same harmonic wave-lengths; but they may differ as regards the members of the series present and their amplitudes and epochs.
We may regard quality, then, as determined by the members of the harmonic series present and their amplitudes and epochs.
If the amplitudes of vibration which thus mutually interfere are moreover equal, the effect is the total mutual destruction of the vibratory motion.
The amplitudes of these tones are proportional to the products of a and b multiplied by X or µ.
The combination tones thus produced in the source should have a physical existence in the air, and the amplitudes of those represented in (35) should be of the same order.
The diffusivity can be deduced from observations at different depths x' and x", by observing the ratio of the amplitudes, which is (x '- x ") for a simple-harmonic wave.
The amplitudes and phases of the temperature waves at different points are observed by taking readings of the thermometers at regular intervals.
The following table gives the period, for various amplitudes a, in terms of that of oscillation in an infinitely small arc about a vertical axis half-way between the points of attachment of the upper string.
The amplitudes of oscilla Ia tion of the various particles have definite ratios to one another, and the phases are in agreement, the absolute amplitude (depending on C) and the phase-constant () being alone arbitrary.
The motion of the system consequent on arbitrary initial conditions may be obtained by superposition of the n normal modes with suitable amplitudes and phases.
Disturbances of the former kind lead to vibrations of harmonic type, whose amplitudes always remain small; but disturbances, whose wave-length exceeds the circumference, result in a greater and greater departure from the cylindrical figure.