Question

For a standing wave, $y=10sin(\frac{\pi }{18}x\left)\cos \right(84\pi t)m$ the distance (in metre) between a node and the next antinode is:

• A. 8.5
• B. 9
• C. 18
• D. 19

Answer 1

Answer: (B)

9

$y=10sin\left(\frac{\pi x}{18}\right)cos\left(84\pi t\right)$
So, $k=\frac{\pi }{18}$
$k=\frac{2\pi }{\lambda }$$\Rightarrow \lambda =\frac{2\pi }{k}$$=\frac{2\pi }{{}^{\pi }{/}_{18}}$$=36m$
Distance between node and antinode is $\frac{\lambda }{4}$$=\frac{36}{4}$$=9m$