Question

The equation of a stationary wave is $y=0.8\text{cos}\left(\frac{\pi x}{20}\right)\text{sin}200\pi t$, where $x$ is in $\text{cm}$ and $t$ is in seconds. The separation between a successive node and antinode will be

• A. $20\text{cm}$
• B. $10\text{cm}$
• C. $40\text{cm}$
• D. $30\text{cm}$

Answer 1

The correct option is B $10\text{cm}$

For the stationary wave given by equation,
$y=0.8\text{cos}\left(\frac{\pi x}{20}\right)\text{sin}\left(200\pi t\right)$
Comparing it with, $y=2\text{A cos kx sin}\omega t$
We get, $k=\frac{\pi }{20}\&\omega =200\pi$
Wavelength of constituent waves is:
$\lambda =\frac{2\pi }{k}=\frac{2\pi }{\left(\frac{\pi }{20}\right)}=40\text{cm}$
The distance between a node & consecutive antinode is
$\Delta x=\frac{\lambda }{4}=\frac{40}{4}=10\text{cm}$