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Two waves are passing through a region in the same direction at the same time. If the equation of these waves are

$\begin{aligned} y_1 & =a \sin \frac{2 \pi}{\lambda}(v t-x) \\ \text { and } \quad y_2 & =b \sin \frac{2 \pi}{\lambda}\left[(v t-x)+x_0\right] \end{aligned}$

then the amplitude of wave for $x_0= \frac{\lambda}{2}$ is-

Option: 1
$\left ( a-b \right )$

Option: 2
$\left ( a+b \right )$

Option: 3
$\sqrt {a^2+b^2}$

Option: 4
None

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