Question

A wave disturbance in a medium is describe by $y(x,t)=0.02\cos (50\pi t+\frac{\pi }{2})\cos \left(10\pi x\right)$ where $x$ and $y$ are in metre and $t$ is in second

• A. A node occurs at $x=0.15m$
• B. An antinode occurs at $x=0.3m$
• C. The speed wave is $5m{s}^{-1}$
• D. The wave length is $0.3m$

Answer 1

The correct option is B An antinode occurs at $x=0.3m$

$\frac{2\pi }{\lambda }=10\pi \Rightarrow \lambda =0.2m$

at $\frac{3}{4}\lambda =\frac{3}{4}\times 0.2=0.15$ there is a node ( ref figure

$K=\frac{w}{v}\Rightarrow 10\pi =\frac{50\pi }{V}$

$\Rightarrow v=5m/s$

from fig an antinode is at $x=0.3m$.