The equation of a stationary wave is $y = 0.8\cos \,\left( {\frac{{\pi x}}{{20}}} \right)\sin 200\,\pi t$, where $x$ is in $cm$ and $t$ is in sec. The separation between consecutive nodes will be..... $cm$
Medium
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(a) On comparing the given equation with standard equation
$y = 2a\sin \frac{{2\pi x}}{\lambda }\cos \,\frac{{2\pi vt}}{\lambda }$
We get $\frac{{2\pi }}{\lambda } = \frac{\pi }{{20}} \Rightarrow \lambda = 40$
Separation between two consecutive nodes = $\frac{\lambda }{2} = \frac{{40}}{2} = 20\,\,cm$
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