When the two waves are in phase, i . e . the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximal, and when they are in anti-phase, i . e . the path difference is equal to half a wavelength, one and a half wavelengths, etc ., then the two waves cancel, and the summed intensity is zero.
32.
As explained in 1882 by Newcomb, the interval between passages of Mercury through the ascending node of its orbit is 87.969 days, and the interval between the Earth's passage through that same longitude is 365.254 days . From the ratio of these values, it can be easily shown that Mercury will make an almost integral number of revolutions about the Sun over intervals of 4, 6, 7, 13, 33, 46, 171 and 217 years.
33.
In fact the shape resonance occurs where the integral number of wavelengths of the particle sit within the potential of the nucleus of radius R . Therefore, the measure of the energies of the shape resonances in the neutron-nucleus scattering have been used in the years from 1947 to 1954 to measure the radii R of the nuclei with the precision of ??0 " 13 cm as it can be seen in the chapter " Elastic Cross Sections " of " A Textbook in Nuclear Physics " by R . D . Evans.
34.
If the perturbation oscillates an integral or half-integral number of times between coming into the horizon and recombination, it appears as an acoustic peak of the cosmic microwave background anisotropy . ( A half-oscillation, in which a dense region becomes a rarefied region or vice versa, appears as a peak because the anisotropy is displayed as a " power spectrum ", so underdensities contribute to the power just as much as overdensities . ) The physics that determines the detailed peak structure of the microwave background is complicated, but these oscillations provide the essence.
