Two progressive waves Y_1 = sin 2 pi left( fr | vedclass

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(C) The resultant displacement $Y$ is given by the superposition principle: $Y = Y_1 + Y_2$.Using the trigonometric identity $\sin(A - B) + \sin(A + B

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$\sqrt{2} \ m$

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(C) The resultant displacement $Y$ is given by the superposition principle: $Y = Y_1 + Y_2$.Using the trigonometric identity $\sin(A - B) + \sin(A + B) = 2 \sin A \cos B$,where $A = \frac{2 \pi t}{0.4}$ and $B = \frac{2 \pi x}{4}$,we get:$Y = 2 \sin \left( \frac{2 \pi t}{0.4} ight) \cos \left( \frac{2 \pi x}{4} ight)$.The amplitude $R$ of the standing wave at any position $x$ is given by $R = |2 \cos \left( \frac{2 \pi x}{4} ight)|$.Substituting $x = 0.5 \ m$:$R = 2 \cos \left( \frac{2 \pi 	imes 0.5}{4} ight) = 2 \cos \left( \frac{\pi}{4} ight)$.Since $\cos \left( \frac{\pi}{4} ight) = \frac{1}{\sqrt{2}}$,we have $R = 2 	imes \frac{1}{\sqrt{2}} = \sqrt{2} \ m$.

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