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
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(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
= $\frac{\lambda }{4} = \frac{{30}}{4} = 7.5$
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