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Wave Reflection and Stationary Waves
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The equation of a stationary wave is $Y=10\sin{\cfrac{\pi x}{4}}\cos{20\pi t}$. The distance between two consecutive nodes in meters is -
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A
4
💡 Explanation:
$Y = 10\sin \dfrac{{\pi x}}{4}\cos \pi t$
At nodles amplitude part is zero.
$\begin{array}{l} \Rightarrow 10\sin \dfrac { { \pi x } }{ 4 } =0 \ \Rightarrow \dfrac { { \pi x } }{ 4 } =0,\pi ,2\pi \ \Rightarrow x=0.x=4,x=8 \end{array}$
$\therefore 4$ is distance between two consultative node.
$\therefore$ Option $A$ is correct.