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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$y=A \sin \left(\frac{20}{3} \pi x\right) \cos (1000 \pi t)$
$\sin \left(\frac{20 \pi}{3} x\right)=\frac{1}{2}$
$\frac{20 x}{3}=\frac{\pi}{6} ; \quad x=\frac{1}{40} m$
Distance $=2 x=\frac{1}{20} m=5 \mathrm{cm}$
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