A) 7.5cm
B) 15cm
C) 22.5 cm
D) 30 cm
Correct Answer: A
Solution :
Given, \[y=u\sin \frac{\pi x}{15}\cos 96\pi t\] For nodes; displacement is zero \[\sin \frac{\pi x}{15}=0\] \[\frac{\pi x}{15}=0,\pi ,2\pi .......\] \[x=0,15,30,\text{ }...\] For antinodes, displacement is maximum \[\sin \frac{\pi x}{15}=1\] \[\frac{\pi x}{15}=\frac{\pi }{2},\frac{3\pi }{2},......\] \[x=\frac{15}{2},\frac{45}{2},.......\] Hence, distance between a node and next antinode \[=\frac{15}{2}-0=\frac{15}{2}=7.5\,cm\]
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