Question

For the stationary wave $y=4\sin \left(\frac{\pi x}{15}\right)\cos (96\pi t)$, the distance between a node and the next antinode is

• A. 7.5
• B. 15
• C. 22.5
• D. 30

Answer 1

Answer: (A)

Comparing given equation with standard equation
$y=2a\sin \frac{2\pi x}{\lambda }\cos \frac{2\pi vt}{\lambda }$ gives us
$\frac{2\pi }{\lambda }=\frac{\pi }{15}$
$\Rightarrow \lambda =30$
Distance between nearest node and antinodes
$=\frac{\lambda }{4}=\frac{30}{4}=7.5$