Question:
Two travelling waves produces a standing wave represented by equation,
$\mathrm{y}=1.0 \mathrm{~mm} \cos \left(1.57 \mathrm{~cm}^{-1}\right) \mathrm{x} \sin \left(78.5 \mathrm{~s}^{-1}\right) \mathrm{t}$
The node closest to the origin in the region $x>0$
will be at $x=$ $\mathrm{cm}$.
Solution:
For node
$\cos \left(1.57 \mathrm{~cm}^{-1}\right) \mathrm{x}=0$
$\left(1.57 \mathrm{~cm}^{-1}\right) \mathrm{x}=\frac{\pi}{2}$
$x=\frac{\pi}{2(1.57)} \mathrm{cm}=1 \mathrm{~cm}$
Ans. $1.00$
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