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  4. The phase difference between two waves reaching a point is π / 2. What is the resultant amplitude if the individual amplitudes are 3 mm 4 mm ?

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Q. The phase difference between two waves reaching a point is $\pi / 2$. What is the resultant amplitude if the individual amplitudes are $3 mm \& 4 mm ?$

Wave Optics

Solution:

According to the relation, $R =\sqrt{ a ^{2}+ b ^{2}+2 ab \cos \phi}$
$R=\sqrt{(3)^{2}+(4)^{2}+2 \times 3 \times 4 \cos \frac{\pi}{2}}$
$R=\sqrt{3^{2}+4^{2}}$
$ \Rightarrow R=\sqrt{9+16}=5 mm$