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Physics-

General

Easy

Question

Four waves are described by equations as follow $Y subscript 1 end subscript equals A c o s invisible function application left parenthesis omega t minus k x right parenthesis$ $Y subscript 2 end subscript equals fraction numerator A over denominator 2 end fraction c o s invisible function application open parentheses omega t minus k x plus fraction numerator pi over denominator 2 end fraction close parentheses$ $Y subscript 3 end subscript equals fraction numerator A over denominator 4 end fraction c o s invisible function application left parenthesis omega t minus k x plus pi right parenthesis$ $Y subscript 4 end subscript equals fraction numerator A over denominator 8 end fraction c o s invisible function application open parentheses omega t minus k x plus fraction numerator 3 pi over denominator 2 end fraction close parentheses$ and their resultant wave is calculated as $Y equals Y subscript 1 end subscript plus Y subscript 2 end subscript plus Y subscript 3 end subscript plus Y subscript 4 end subscript text such as end text$ $Y equals A to the power of 1 end exponent c o s invisible function application left parenthesis omega t minus k x plus ϕ right parenthesis$ then………..(symbols have their usual meanings)

$A^{1} = \frac{\sqrt{5} A}{8} ϕ = {t a n}^{- 1} (\frac{1}{4})$
$A^{1} = \frac{2 \sqrt{5} A}{8} ϕ = {t a n}^{- 1} (\frac{1}{3})$
$A^{1} = \frac{3 \sqrt{5} A}{8} ϕ = {t a n}^{- 1} (\frac{1}{2})$
$A^{1} = \frac{4 \sqrt{5} A}{8} ϕ = {t a n}^{- 1} (1)$

The correct answer is: $A to the power of 1 end exponent equals fraction numerator 3 square root of 5 A over denominator 8 end fraction ϕ equals t a n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses$

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