SUPERPOSITION OF WAVES: Let us consider what happens when two different waves cross a particle of a medium simultaneously. Each wave behaves as if the opposite wave isn’t present and would set the particle into Simple harmonic motions. therefore the particle is about into two S.H.M.’s thanks to the 2 waves. Hence the resultant displacement of the particle at any instant would be adequate to the sum of the displacements thanks to both the waves. this is often called as principle of superposition of waves which states: When two or more waves travelling through a medium reach a point of the medium simultaneously, each wave produces its own displacement at that time independently of the others. Hence the resultant displacement at that time is adequate to the resultant of the displacements thanks to all the waves.
This effect produced thanks to superposition of waves is named interference and it’s true just in case and longitudinal also as transverse waves. If two wav having an equivalent amplitude and same frequency and travelling within the same direction, arrive simultaneousiy at some extent of the medium, then if the 2 waves arrive in phase, the resultant amplitude at that time is maximum and if the 2 waves reach the purpose out of phase, then the resultant amplitude at that time is minimum.
Thus if two transverse waves superimpose in phase then a crest thanks to one wave coincides with the crest thanks to the opposite or the trough thanks to one wave coincides with the trough thanks to the opposite the resultant amplitude at that time is maximum and is named constructive interference. If a crest thanks to one wave coincides with the trough thanks to the opposite or vice-versa the resultant amplitude thanks to interference is minimun and is named destructive interference, as shown in Fig. (7.6). When two sound waves reach a p0int in phase, the rarefaction thanks to one coincides with the rarefaction thanks to the opposite or the compression thanks to one coincides with the compression thanks to the opposite , then the resultant amplitude at that time is maximum and hence the intensity of sound is maximum. On the opposite hand, if the waves arriving at that time are out of phase, the compression thanks to one wave coincides with a rarefaction of the opposite wave and vice-versa, then the resultant amplitude is minimum at that time and therefore the resultant intensity of sound is minimum.
The superposition of two sound waves are often demonstrated by the Quincke’s tube experiment.
Quincke’s tube experiment:
The apparatus consists of a U-tube ABC, about 2 cm in diameter which has two side openings at D and E. A second U-tube, MNQ closely fits into ABC and may be pushed into or pulled out of ABC. (Fig. 7.7). Thus the effective length of the proper branch DNE are often altered and frequency generator is held at the opening D. The sound waves follow the 2 branches DBE and DNE and meet at E. The ear of a listener is Situated at E. Initially, the tube MNQ, is so adjusted, that the paths DBE and DNE are of equal lengths or the trail difference between the waves travelling along DBE and DNE is zero. Then the intensity of sound heard by the listener at E is maximum. The moving tube MNQ is then slowly pulled out of ABC. it’s found that the intensity of sound heard by the listener becomes zero when the trail difference between the waves travelling along the 2 branches becomes 1lyamda/2. On further coitus interruptus the tube MNQ, the sound intensity is again found to become maximum when the trail difference between the waves travelling along the 2 branches becomes lyamda. generally whenever the trail difference becomes 0, 1lyamda, 2lyamda etc.
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