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Two waves are represented by
$y_{1} = asin (ωt + π / 6) and y_{2} = acos ωt What will be their resultant amplitude ?$

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$α$

$\sqrt{2} a$

$\sqrt{3} a$

$2 α$

answer is C.

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Detailed Solution

$a \equiv {[a_{1}^{2} + a_{2}^{2} + 2 a_{1} a_{2} \cos ϕ]}^{1 / 2} = {[a^{2} + a^{2} + 2 a \cdot a \cdot \cos π / 3]}^{1 / 2} = {[2 a^{2} + 2 a^{2} \cos π / 3]}^{1 / 2} = a [2 + 1]^{1 / 2} = \sqrt{3} \cdot a$

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