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. $20 \,cm$
• B. $10\, cm$
• C. $40 \,cm$
• D. $30\, cm$

Answer 1

Answer: (A)

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