Wave Interference
The physics of waves describes their behavior and wave phenomena such as reflection, refraction, dispersion, and interference. Interference is the phenomenon observed when two traveling wave trains coexist in the same medium. Consider single frequency waves described by a sine function and the following quantities: a period T, or the time required to complete a full cycle, a frequency ƒ, which is the reciprocal of the period, an amplitude A, which is the maximum displacement from the equilibrium position and a wavelength &lgr; which is the distance between two wave crests, or positions of maximum amplitude. If the sine crests of two waves traveling in opposite directions through the same medium completely overlap (i.e., become in-phase) their amplitudes add and the interference is referred to as constructive interference. A single wave with double amplitude is observed in the medium. If the two wave crests become half a period or 180° out-of-phase, their amplitudes then subtract and the interference is called destructive interference. The interfering waves have the same maximum displacement, but in opposite directions and thus, their amplitudes cancel out, or subtract if they were not equal before overlap. The occurrence of interference does not modify the properties of the individual waves, nor does it change their path. The shape of the wave resulting from interference is determined by the principle of superposition, which states that when wave interference occurs, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.
An example of interference is provided by the tuning fork, which creates an outward traveling pressure wave when it is struck.
One wave component has a pressure higher than atmospheric pressure, and another component has a lower pressure. At some specific angles, the high pressure areas of the two waves interfere constructively and a louder sound is heard. At other angles, the high pressure part of one wave coincides with the low pressure part of the other wave, resulting in destructive interference and a lower sound. Another example of wave interference is illustrated by the beat phenomenon which occurs when two sound waves of different frequency alternate constructive and destructive interference. This produces a sound which alternates between soft and loud, or beats. The beat frequency is equal to the absolute value of the difference in frequency of the two waves and if it lies in the mid-frequency region, it can be heard by the human ear as a third tone, called a subjective tone. Such tones are used in multiphonics applications. Another use of beat frequencies is in police radar speed detectors which bounce microwave radiation off of speeding vehicles and detect the reflected waves. These waves are shifted in frequency as a result of the Doppler effect, and the beat frequency between the emitted and reflected waves measures the speed of the moving car.
An important consequence of interference in wave physics is that interference is the phenomenon which gives rise to standing waves. Standing waves are the characteristic signatures of a specific vibrational pattern generated within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source in such a way that nodes along the medium appear to be standing still.
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