Question

Since sinusoidal waves are cyclical, a particular phase difference between two waves is identical to that phase difference plus a cycle. For example, if two waves have a phase difference of \frac{\pi}{4}, the interference effects would be the same as if the two waves had a phase difference of \frac{\pi}{4} + 2\pi. The complete criterion for constructive interference between two waves is therefore written as follows:
{\rm phase\ difference} = 0 + 2 \pi n \qquad {\rm for\ any\ integer}\ n
Write the full criterion for destructive interference between two waves.

Answer 1

Answer:

For destructive interference phase difference is

$(2n+1)\pi$ where n∈ Whole numbers

Explanation:

For sinusoidal wave the interference affects the resultant intensity of the waves.

In the given example we have two waves interfering at a phase difference of $\frac{\pi}{4}$ would lead to a constructive interference giving maximum amplitude at at the RMS value of the amplitude in resultant.

Also the effect is same as having a phase difference of  $( \frac{\pi}{4} + 2\pi)$ because after each 2π the waves repeat itself.

In case of destructive interference the waves will be out of phase i.e. the amplitude vectors will be equally opposite in the direction at the same place on the same time as shown in figure.

They have a phase difference of $\pi$ or which is same as $(2\pi+\pi)$

Generalizing to:

a phase difference of $(2n+1)\pi$ where n∈ {W}

{W}= set of whole numbers.