Two waves are passing through a region in the same direction at the same time. If the equations of these…
Two waves are passing through a region in the same direction at the same time. If the equations of these waves are $y_1 = a \sin \frac{2\pi}{\lambda} (vt - x)$ and $y_2 = b \sin \frac{2\pi}{\lambda} [(vt - x) + x_0]$, then the amplitude of the resultant wave for $x_0 = \lambda / 2$, is
$|a - b|$
$(a + b)$
zero
$\sqrt{a^2 + b^2}$
Solution
Path difference of $x_0 = \frac{\lambda}{2}$ corresponds to a phase difference of $\pi$. They will interfere destructively and resultant amplitude is $| a - b |$.