Question

The separation between a node and an antinode in the stationary wave $y=20\sin \left(2x\right)\cos 400\pi t$ is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{8}$

Answer 1

The correct option is B $\frac{\pi }{4}$

Compare the above equation with standard equation:
$y=2A\sin \frac{2\pi x}{\lambda }\cos 2\pi ft$
$A=10$, $\lambda =\pi$, $f=200Hz$
The separation between a node and an antinode in the stationary wave usually $\frac{\lambda }{4}=\frac{\pi }{4}$