Question
Explain destructive interference using proper $($appropriate$)$ example.
✓
Answer
$\rightarrow $ As shown in fig.$(c)$, consider two needles $S _1$ and $S _2$ moving periodically up and down in an identical fashion in a trough of water.
$\rightarrow $Here, they produce two water waves, and at a particular point, the phase difference between the displacements produced by each of the waves does not change with time.
$\rightarrow $When this happens, the two sources $($here $S_1$ and $S _2 )$ are said to be coherent sources,
$\rightarrow $As shown in fig. $(a),$ consider a point R for which,
$S _2 R - S _1 R =-2.5 \lambda$
$\rightarrow $The waves emanating from $S _1$ will arrive exactly two and a half cycles later than the waves from $S _2$. Hence the wave coming from $S _2$ will be ahead in phase by $5 \pi rad$.
$\rightarrow $Hence, displacement produced by $S_1$ is given by
$_1=a \cos \omega t$
$\rightarrow $then the displacement produced by $S _2$ will be given by,
$y_2=a \cos (\omega t+5 \pi)$
$y_2=-a \cos \omega t$
$\rightarrow $Resultant (/ Net) displacement at $R ,$
$\begin{aligned} y & =y_1+y_2 \\ \therefore y & =a \cos \omega t+(-a \cos \omega t) \\ \therefore y & =0\end{aligned}$
$\rightarrow $As the net displacement at point $R$ is zero, the resultant intensity at R will also be zero. $($That is because, here, the two displacement are now out of phase and they will cancel out to give zero intensity.$)$
$\rightarrow $This is referred to as Destructive interference.
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