Two coherent waves are represented by y1=a1cosωt and y2=a2cosπ2−ωt. Their resultant intensity after interference will be proportional to

y1=a1cosωty2=a2cosπ2−ωt=a2cosωt−π2Then the resultant isa=a12+a22+2a1a2cos⁡π2a2=a12+a22Iαa2 ⇒I=ka2I=ka12+a22

Two coherent waves are represented by y1=a1cosωt and y2=a2cosπ2−ωt. Their resultant intensity after interference will be proportional to

y1=a1cosωty2=a2cosπ2−ωt=a2cosωt−π2Then the resultant isa=a12+a22+2a1a2cos⁡π2a2=a12+a22Iαa2 ⇒I=ka2I=ka12+a22

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Two coherent waves are represented by $y_{1} = a_{1} \cos ω t$ and $y_{2} = a_{2} \cos [\frac{π}{2} - ω t]$ . Their resultant intensity after interference will be proportional to

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$a_{1} - a_{2}$

$a_{1} + a_{2}$

${a_{1}}^{2} - {a_{2}}^{2}$

${a_{1}}^{2} + {a_{2}}^{2}$

answer is D.

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$y_{1} = a_{1} \cos ω t$

$y_{2} = a_{2} \cos [\frac{π}{2} - ω t]$ = $a_{2} \cos [ω t - \frac{π}{2}]$

Then the resultant is

$a = \sqrt{a_{1}^{2} + a_{2}^{2} + 2 a_{1} a_{2} \cos \frac{π}{2}}$

$a^{2} = {a_{1}}^{2} + {a_{2}}^{2}$

$I α a^{2}$ $\Rightarrow$ $I = k a^{2}$

$I = k (a_{1}^{2} + a_{2}^{2})$

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Two coherent waves are represented by y1=a1cosωt and y2=a2cosπ2−ωt. Their resultant intensity after interference will be proportional to

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Two coherent waves are represented by $y_{1} = a_{1} \cos ω t$ and $y_{2} = a_{2} \cos [\frac{π}{2} - ω t]$ . Their resultant intensity after interference will be proportional to