Explanation

(b) $x_{1} = a\sin{(\omega \times 1)} = a\sin\omega$
and $x_{2} = a\sin{(\omega \times 2)} - a\sin\omega$
$\frac{x_{2}}{x_{1}} = \frac{\sin{(2\omega) - \sin\omega}}{\sin\omega}$
$= \sin 2 \times (2\pi/8) - \sin{2\pi/8}$
$= \frac{1 - (1/\sqrt{2})}{(1/\sqrt{2})} = \frac{\sqrt{2} - 1}{1}$
Or $\frac{x_{1}}{x_{2}} = \frac{1}{\sqrt{2} - 1} = \frac{\sqrt{2} + 1}{\left( \sqrt{2} - 1 \right)(\sqrt{2} + 1)}$
$= \frac{\sqrt{2} + 1}{2 - 1}$
$= 2.414 = 2.4$