question_answer

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.             \[=\frac{\lambda }{4}=\frac{30}{4}=7.5cm\]