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# Wave Interference | Constructive and Destructive Interference

July 31, 2022

Wave Interference is the phenomenon where two waves combine by applying a displacement at any one point in space and time to form waves of greater, lesser, or equal amplitude.

## Interference

The phenomenon of superposition of two waves of the same frequency and traveling in the same direction is called interference of waves.

The experimental arrangement to observe the interference effect in sound waves.

## Experiment for Interference

Two loud speakersS1, S2 are taken as two sources of harmonic sound waves of a fixed frequency. The waves are produced by an audio generator. A microphone is connected to a sensitive cathode ray oscilloscope (CRO).

The CRO detects the input signal into the waveform on its screen. The microphone is placed at different positions turn by turn in front of the loudspeakers to observe the signal. At points, P1 P3, and P5 large signals are seen on CRO but at points P3, and P4 no signal is seen on CRO.

The compressions and rarefactions are alternately emitted by both speakers in the above fig continuous lines show the compression and dotted lines show rarefactions. At points, p1 p3, and p5compression meet with compression and a rarefaction meets a rarefaction. As a result, the displacement of two waves added up and a large resultant displacement is produced which is seen on the CRO screen.

At points, P2 and P4 compression meet with a rarefaction canceling each otherâ€™s effect. The resultant displacement becomes zero.

For Constructive Interference:

The path difference Î”s between the waves at the point P1 is

Î”s=s2 p1-s1P1

=4 Î»/2- 3 Î»/2=Î»

Similarly the path difference at points P3 and P5is zero and â€“Î» respectively.

## Constructive Interference

When path difference is an integral multiple of the wavelength, the displacements of the two waves are added up. This effect is called constructive interference”. The condition for constructive interference can be written as.

Î”s=n Î»

N=0Â±1Â±2Â±3,â€¦

For Destructive interference

The path difference Î”s between the waves at point P2 is

Î”s=s2 P2-s1P2

=4 Î» -3 Î» /2=1/2 Î»

Similarly at P4the path difference is -1/2 Î».

## Destructive Interference

When path difference is an odd integral multiple of half the wavelength, the displacement of two waves cancels each other. This effect is called destructive interference.

The condition for destructive interference can be written as

Î”s= (2n+1) Î»/2

n=0, Â±1, Â±2, Â±3,â€¦

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