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

Given that $\mathrm{y}=4\sin \left(\frac{\mathrm{\pi X}}{15}\right)\cos \left(96\mathrm{\pi t}\right)$
The equation for stationary wave is
$\mathrm{y}=\mathrm{asin}\left(\frac{2\mathrm{\pi x}}{\mathrm{\lambda }}\right)\cos \left(\frac{2\mathrm{\pi vt}}{\mathrm{\lambda }}\right)$
$\text{ Comparing the two equations, we get }\mathrm{\lambda }=30$
Distance between Lode and next anti node

$=\frac{\mathrm{\lambda }}{4}=\frac{30}{4}=7\cdot 5$