Q. 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
Explanation
(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
$= \frac{\lambda}{4} = \frac{30}{4} = 7.5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.