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 cm and $t$ is in s. The separation between consecutive nodes will be

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

Answer 1

Answer: (A)

Standard equation
$y=A\cos \frac{2\pi x}{\lambda }\sin \frac{2\pi vt}{\lambda }$
By comparing this equation with given equation.
$\frac{2\pi x}{\lambda }=\frac{\pi x}{20}$
$\Rightarrow \lambda =40cm$
Distance between two nodes $=\lambda /2=20cm$.