interference

(1) In biology, the influence of the crossover of homologous chromosomes in one area on the appearance of new crossovers in neighboring areas. Most often this type of interference inhibits the appearance of a new crossover in a neighboring area; hence, in experiments the percentage of double-crossover individuals as a rule turns out to be lower than that theoretically expected. Double crossover is particularly strongly suppressed by interference when there are small distances between the genes.

(2) In medicine, interference of viruses is the suppression by one virus of the effect of another when there is a mixed infection.In such cases the first virus is called the interfering one, and the second is called the pretender.

(of waves), superposition of two or more waves in space, producing an increase or decrease in the amplitude of the resulting wave. Interference is characteristic of all waves, regardless of their nature: waves on the surface of a liquid, elastic waves (such as sound waves), and electromagnetic waves (such as radio or light waves).

If two waves are propagating through space, then the resulting oscillation at every point is the geometric sum of the oscillations corresponding to each of the component waves. This “superposition principle” is usually strictly obeyed and is violated only in the propagation of waves in a medium if the amplitude (intensity) of the waves is very large. Wave interference is possible if the waves are coherent.

The simplest case of interference is the addition of two waves of identical frequency and phase. In this case, if the oscillations take place according to a sine (harmonic) law, the amplitude of the resultant wave at any point in space is

where A₁ and A₂ are the amplitudes of the component waves and ϕ is the phase difference between the waves at the point in question. If the waves are coherent, the phase difference ϕ remains unchanged at the given point but may change from point to point, leading to a distribution of the amplitudes of the resultant waves with alternating maximums and minimums. If the amplitudes of the component waves are the same (that is, if A₁A₂), the maximum amplitude is equal to twice the amplitude of each wave, and the minimum amplitude is equal to zero. The geometric loci of equal phase difference, which specifically corresponds to the maximums or minimums, are surfaces that depend on the properties and location of the sources emitting the component waves. In the case of two point sources emitting spherical waves, the surfaces are hyperboloids of rotation.

Another important instance of interference is the superposition of two plane waves propagating in opposite directions (for example, incident and reflected waves). In this case standing waves are produced.

The average values of the energy flux of the wave over the period is proportional to the square of the amplitude. Therefore, it follows from the equation for the resultant amplitude that interference involves a redistribution of the energy flux of the wave in space. The distribution of amplitudes with alternating minimums and maximums, which is characteristic of interference, remains stationary in space or moves so slowly that the maximums and minimums are not displaced by a quantity comparable to the distance between them during the time required for the observation, and it may be observed only when the waves are coherent. If the waves are incoherent, then the phase difference ϕ changes rapidly and at random, assuming all possible values, so that the average value of cos ϕ is zero. In this case, the average value of the amplitude of the resultant wave is found to be the same at different points, the maximums and minimums are blurred, and the interference pattern disappears. In this case, the mean square of the resultant amplitude is equal to the sum of the mean squares of the amplitudes of the component waves—that is, superposition of waves involves the addition of the energy fluxes or intensities.

The main features of the interference phenomenon described above apply equally to elastic and electromagnetic waves. However, although coherence of sonic and radio waves is easily achieved (for example, by using the same current to feed various antennas or speakers), before the development of the laser coherent light beams could be produced only by the same light source, using special methods. Another essential difference between the methods of interference production involving sonic and radio waves on the one hand and light waves on the other is related to the size of the emitters. The size of the sonic and radio-wave emitters is almost always comparable with the length of the emitted wave, whereas in the case of light waves, the size of the source is almost always large in comparison with the wavelength. For this reason, the problem of the extent of the source plays a significant role in the interference of light waves. Because of these special features, light interference may be observed only under special conditions.

Wave interference is of great importance in both research and technology. Since a definite relationship exists among the wavelength, the path difference of interfering rays, and the position of maximums and minimums, knowledge of the path difference of the interfering waves makes possible determination of the wavelength from the positions of the minimums and maximums and, conversely, knowledge of the wavelength makes possible determination of the path difference of the rays (that is, measurement of distances) from the positions of the maximums and minimums. Instruments using wave interference include optical interferometers, radio interferometers, and interferential radio range finders.