Question

Two travelling waves produces a standing wave represented by equation, $y=1.0\text{mm}\cos \left[\right(1.57{\text{cm}}^{-1}\left)x\right]\sin \left[\right(78.5{\text{s}}^{-1}\left)t\right]$. The node closest to the origin in the region $x>0\text{cm}$ will be at $x=$____$\text{cm}$.

• A. 1.00
• B. 1.0
• C. 1

Answer 1

Answer: (A), (B), (C)

Given:

$y=1.0\text{mm}\cos \left[\right(1.57{\text{cm}}^{-1}\left)x\right]\sin \left[\right(78.5{\text{s}}^{-1}\left)t\right]$

For nodes,

$\cos \left[\right(1.57{\text{cm}}^{-1}\left)x\right]=0$

$\Rightarrow \left(1.57{\text{cm}}^{-1}\right)x=\frac{\pi }{2}$

$\Rightarrow x=1\text{cm}$