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 $\frac{2\pi }{\lambda }=\frac{\pi }{2}$
$\Rightarrow$ $\lambda =40cm$
So, separation between two nodes $=\frac{\lambda }{2}=20cm$