A stationery wave is represented by $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$, where $x \& y$ are in $c m$ and $t$ in second. The distance between two successive antinodes is

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Aicharya · Accepted Answer

Given equation for stationary wave, $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$
Comparing this equation with standard stationary wave equation, $y=2 A \sin \left(\frac{2 \pi x}{\lambda}\right) \cdot \cos \left(\frac{2 \pi}{\lambda} t\right)$ $\begin{aligned} & \text { We get, } \\ & \frac{2 \pi}{\lambda}=\frac{\pi}{6} \\ & \therefore \quad \lambda=12 \mathrm{~cm} \end{aligned}$ $\therefore \quad$ Distance between two successive antinodes $=\frac{\lambda}{2}=6 \mathrm{~cm}$

A stationery wave is represented by $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$, where $x \& y$…

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