Explanation

(b) Here, $y_{1} = 0.05\sin{(3\pi t - 2x)}$
$y_{2} = 0.05\sin{(3\pi t + 2x)}$
According to superposition principle, the resultant displacement is
$y = y_{1} + y_{2}$
$= 0.05\left\lbrack \sin{(3\pi t - 2x)} + \sin{(3\pi t + 2x)} \right\rbrack$
$y = 0.05 \times 2\sin{3\pi t\cos{2x}}$
$y = \left( 0.01\cos{2x} \right)\sin{2\pi t} = R\sin{3\pi t}$
Where $R = 0.1\ \cos{2\ x =}$ amplitude of the resultant standing wave.
At $x = 0.5\ m$
$R = 0.1\cos{2x = 0.1\cos{2 \times 0.5}}$
$= 0.1\cos{1(radian) = 0.1\cos\frac{180{^\circ}}{\pi}}$
$= 0.1\cos{57.3{^\circ}}$
$R = 0.1 \times 0.54m = 0.054m = 5.4cm$.