A standing wave y = A sin left( frac{20}{3} p | vedclass

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(C) The equation of the standing wave is $y = A \sin \left( \frac{20}{3} \pi x \right) \cos (1000 \pi t)$.The amplitude of oscillation at any point $x

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$5$

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(C) The equation of the standing wave is $y = A \sin \left( \frac{20}{3} \pi x \right) \cos (1000 \pi t)$.The amplitude of oscillation at any point $x$ is given by $A(x) = |A \sin \left( \frac{20}{3} \pi x \right)|$.We are looking for points where the amplitude is $A/2$,so $|A \sin \left( \frac{20}{3} \pi x \right)| = A/2$,which implies $\sin \left( \frac{20}{3} \pi x \right) = \pm 1/2$.For the first positive value,$\frac{20}{3} \pi x = \frac{\pi}{6}$,which gives $x_1 = \frac{3}{120} = \frac{1}{40} \ m$.For the point on the other side of the node (at $x=0$),the position is $x_2 = -\frac{1}{40} \ m$.The distance between these two points is $|x_1 - x_2| = |\frac{1}{40} - (- \frac{1}{40})| = \frac{2}{40} = \frac{1}{20} \ m$.Converting to centimeters: $\frac{1}{20} \ m = 0.05 \ m = 5 \ cm$.

$A$ standing wave $y = A \sin \left( \frac{20}{3} \pi x \right) \cos (1000 \pi t)$ is maintained in a taut string,where $y$ and $x$ are expressed in meters. The distance between the successive points oscillating with the amplitude $A/2$ across a node is equal to ... $cm$.

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