Question

The equation of a stationary wave is $ y=0.8\,\cos \,\left( \frac{\pi x}{20} \right)\,\sin \,200\,\pi t $ where $x$ is in and $t$ is in sec. The separation between consecutive nodes will be

• A. 20 cm
• B. 10 cm
• C. 40 cm
• D. 30 cm

Answer 1

Answer: (A)

Given equation is $ y=0.8\cos \left( \frac{\pi x}{20} \right)\,\sin \,\,200\pi t $
Comparing it with $ y=a\,\cos \frac{2\pi x}{\lambda }\sin \,\omega t, $
we get $ \frac{2\pi }{\lambda }=\frac{\pi }{2} $
$ \Rightarrow $ $ \lambda =40\,cm $
So, separation between two nodes $ =\frac{\lambda }{2}=20\,cm $