A) 2 cm
B) 4 cm
C) 8 cm
D) 16 cm
Correct Answer: A
Solution :
Key Idea: Distance between consecutive nodes is half of wavelength. The standard equation of wave is \[y=a\,\sin \,kx\,\cos \omega \,t\] ... (i) where a is amplitude and co is angular velocity. Given equation is \[y=5\sin \left( \frac{\pi x}{2} \right)\cos 4\pi t\] ... (ii) Comparing Eq. (i) with Eq. (ii), we get \[k=\frac{2\,\pi }{\lambda }=\frac{\pi }{2}\] \[\Rightarrow \] \[\lambda =4\,cm\] Hence, distance between two consecutive nodes is N = Node \[=\frac{\lambda }{2}=\frac{4}{2}=2\,cm\]You need to login to perform this action.
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