A) 1.5cm
B) 3 cm
C) 6 cm
D) 4 cm
Correct Answer: B
Solution :
Key Idea: The separation between two adjacent nodes is half of the wavelength. The standard equation of stationary wave is \[y=2a\sin \frac{2\pi x}{\lambda }\cos \frac{2\pi t}{T}\] ...(1) where a is amplitude,\[\lambda \]is wavelength and T is periodic time. Given, equation is \[y=5\sin \frac{\pi x}{3}\cos 40\pi t\] ?. (2) Comparing Eq. (1) with Eq. (2), we get \[\frac{2\pi x}{\lambda }=\frac{\pi x}{3}\] \[\Rightarrow \] \[\lambda =6\,cm\] Distance between adjacent nodes is \[\frac{\lambda }{2}=\frac{6}{2}=3\,cm\]You need to login to perform this action.
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