For the stationary wave \[Y=4\,\sin \,\left( \frac{\pi x}{15} \right)\cos \,(96\pi t),\] (X and Y are in cm and t in secondary the distance between a node and the next anti-node is:
A) \[7.5\,cm\]
B) \[15\,cm\]
C) \[22.5\,cm\]
D) \[30\,cm\]
Correct Answer:
A
Solution :
As, \[r=\frac{2\pi }{\lambda }=\frac{\pi }{15}\] \[\lambda =30\,cm\] N and A are the nodes and anti-nodes respectively. Distance between a node and next antinode. \[=\frac{\lambda }{4}=\frac{30}{4}=7.5cm\]