Two waves of same frequency but amplitudes equal to $a$ and $2 a$ travelling in the same direction superimpose out of phase. The resultant amplitude will be

\sqrt{a^{2} + 2 a^{2}}

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3 a

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2 a

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a

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Solution

The correct option is D $a$
The amplitude of the resultant wave is
$x_{0}^{'} = \sqrt{a^{2} + (2 a)^{2} + 2 a \times 2 a cos (ϕ)}$ , here the angle between the two propagating waves is $ϕ = π$ .
Hence $x_{0}^{'} = \sqrt{a^{2} + (2 a)^{2} + 2 a \times 2 a cos (π)} = \sqrt{a^{2} + (2 a)^{2} - 2 a \times 2 a} = a$

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Two waves of same frequency but amplitudes equal to a and 2a travelling in the same direction superimpose out of phase. The resultant amplitude will be

The correct option is D aThe amplitude of the resultant wave is x′0=√a2+(2a)2+2a×2acos(ϕ), here the angle between the two propagating waves is ϕ=π. Hence x′0=√a2+(2a)2+2a×2acos(π)=√a2+(2a)2−2a×2a=a

Two waves of same frequency but amplitudes equal to $a$ and $2 a$ travelling in the same direction superimpose out of phase. The resultant amplitude will be